Relevant bibliographies by topics / Combinatorial representation theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Combinatorial representation theory'

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Published: 25 May 2024

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Journal articles on the topic "Combinatorial representation theory"

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Ibarra, Andoni, and Thomas Mormann. "Una teoría combinatoria de las representaciones científicas." Crítica (México D. F. En línea) 32, no. 95 (2000): 3–46. http://dx.doi.org/10.22201/iifs.18704905e.2000.874.

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The aim of this paper is to introduce a new concept of scientific representation into philosophy of science. The new concept -to be called homological or functorial representation- is a genuine generalization of the received notion of representation as a structure preserving map as it is used, for example, in the representational theory of measurement. It may be traced back, at least implicitly, to the works of Hertz and Duhem. A modern elaboration may be found in the foundational discipline of mathematical category theory. In contrast to the familiar concepts of representations, functorial re
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Malinin, Dmitry. "One combinatorial construction in representation theory." European Journal of Combinatorics 80 (August 2019): 287–95. http://dx.doi.org/10.1016/j.ejc.2018.02.007.

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HSIEH, CHUN-CHUNG. "FIRST NON-VANISHING SELF-LINKING OF KNOTS (I) COMBINATORIC AND DIAGRAMMATIC STUDY." Journal of Knot Theory and Its Ramifications 20, no. 12 (2011): 1637–48. http://dx.doi.org/10.1142/s0218216511009510.

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In this paper, following the scheme of [Borromean rings and linkings, J. Geom. Phys.60 (2010) 823–831; Combinatoric and diagrammatic study in knot theory, J. Knot Theory Ramifications16 (2007) 1235–1253; Massey–Milnor linking = Chern–Simons–Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903], we study the first non-vanishing self-linkings of knots, aiming at the study of combinatorial formulae and diagrammatic representation. The upshot of perturbative quantum field theory is to compute the Feynman diagrams explicitly, though it is impossible in general. Along this line in this paper
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Bremner, Murray R., Mikelis G. Bickis, and Mohsen Soltanifar. "Cayley’s hyperdeterminant: A combinatorial approach via representation theory." Linear Algebra and its Applications 437, no. 1 (2012): 94–112. http://dx.doi.org/10.1016/j.laa.2012.01.037.

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SHAI, OFFER. "The multidisciplinary combinatorial approach (MCA) and its applications in engineering." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 15, no. 2 (2001): 109–44. http://dx.doi.org/10.1017/s0890060401152030.

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The current paper describes the Multidisciplinary Combinatorial Approach (MCA), the idea of which is to develop discrete mathematical representations, called “Combinatorial Representations” (CR) and to represent with them various engineering systems. During the research, the properties and methods embedded in each representation and the connections between them were investigated thoroughly, after which they were associated with various engineering systems to solve related engineering problems. The CR developed up until now are based on graph theory, matroid theory, and discrete linear programm
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Armenta, Marco, and Pierre-Marc Jodoin. "The Representation Theory of Neural Networks." Mathematics 9, no. 24 (2021): 3216. http://dx.doi.org/10.3390/math9243216.

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In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical object that we represent using a network quiver. Furthermore, we show that network quivers gently adapt to common neural network concepts such as fully connected layers, convolution operations, residual connections, batch normalization, pooling operations and even randomly wired neural networks. We show that this mathematical representation is by no means an app
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Griffeth, Stephen. "Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r, p, n)." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (2010): 419–45. http://dx.doi.org/10.1017/s0013091508000904.

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AbstractThis paper aims to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category $\mathcal{O}$ for the rational Cherednik algebra of type G(r, p, n). As a first application, a self-contained and elementary proof of the analogue for the groups G(r, p, n), with r > 1, of Gordon's Theorem (previously Haiman's Conjecture) on the diagonal co-invariant ring is given. No restriction is imposed on p; the result for p ≠ r has been proved by Vale using a technique analogous to Gordon's. Because of the combinatorial application to Haiman's Conj
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Capparelli, Stefano, Arne Meurman, Andrej Primc, and Mirko Primc. "New partition identities from \(C^{(1)}_\ell\)-modules." Glasnik Matematicki 57, no. 2 (2022): 161–84. http://dx.doi.org/10.3336/gm.57.2.01.

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In this paper we conjecture combinatorial Rogers-Ramanu­jan type colored partition identities related to standard representations of the affine Lie algebra of type \(C^{(1)}_\ell\), \(\ell\geq2\), and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras.
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Vershik, A. M., and N. V. Tsilevich. "On the relationship between combinatorial functions and representation theory." Functional Analysis and Its Applications 51, no. 1 (2017): 22–31. http://dx.doi.org/10.1007/s10688-017-0165-4.

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Proctor, Robert A. "A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group." Canadian Journal of Mathematics 42, no. 1 (1990): 28–49. http://dx.doi.org/10.4153/cjm-1990-002-1.

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This paper is concerned with a combinatorial construction which mysteriously “mimics” or “models” the decomposition of certain reducible representations of orthogonal groups. Although no knowledge of representation theory is needed to understand the body of this paper, a little familiarity is necessary to understand the representation theoretic motivation given in the introduction. Details of the proofs will most easily be understood by people who have had some exposure to Schensted's algorithm or jeu de tacquin.
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Dissertations / Theses on the topic "Combinatorial representation theory"

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Kreighbaum, Kevin M. "Combinatorial Problems Related to the Representation Theory of the Symmetric Group." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1270830566.

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Liu, Xudong. "MODELING, LEARNING AND REASONING ABOUT PREFERENCE TREES OVER COMBINATORIAL DOMAINS." UKnowledge, 2016. http://uknowledge.uky.edu/cs_etds/43.

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In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representatio
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Faitg, Matthieu. "Mapping class groups, skein algebras and combinatorial quantization." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS023/document.

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Les algèbres L(g,n,H) ont été introduites par Alekseev-Grosse-Schomerus et Buffenoir-Roche au milieu des années 1990, dans le cadre de la quantification combinatoire de l'espace de modules des G-connexions plates sur la surface S(g,n) de genre g avec n disques ouverts enlevés. L'algèbre de Hopf H, appelée algèbre de jauge, était à l'origine le groupe quantique U_q(g), avec g=Lie(G). Dans cette thèse nous appliquons les algèbres L(g,n,H) à la topologie en basses dimensions (groupe de difféotopie et algèbres d'écheveaux des surfaces), sous l'hypothèse que H est une algèbre de Hopf de dimension f
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Newhouse, Jack. "Explorations of the Aldous Order on Representations of the Symmetric Group." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/35.

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The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young
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Assunção, Guilherme Puglia. "Representações retangulares de grafos planares." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-07052012-164622/.

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Uma representação retangular de um grafo plano G é uma representação de G, onde cada vértice é desenhado como um retângulo de modo que dois retângulos devem compartilhar algum segmento de seus lados se e somente se existe uma aresta em G entre os vértices correspondentes aos retângulos. Ainda, a representação de G deve formar um retângulo e não deve existir buracos, ou seja, toda região interna deve corresponder a algum vértice de G. Um desenho retangular de um grafo plano H é um desenho de H, onde todas as arestas são desenhadas como segmentos horizontais ou verticais. Ainda, todas as
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Teff, Nicholas James. "The Hessenberg Representation." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4919.

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The Hessenberg representation is a representation of the symmetric group afforded on the cohomology ring of a regular semisimple Hessenberg variety. We study this representation via a combinatorial presentation called GKM Theory. This presentation allows for the study of the representation entirely from a graph. The thesis derives a combinatorial construction of a basis of the equivariant cohomology as a free module over a polynomial ring. This generalizes classical constructions of Schubert classes and divided difference operators fo
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Wolfgang, Harry Lewis. "Two interactions between combinatorics and representation theory : monomial immanants and Hochschild cohomology." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43461.

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Meinel, Joanna [Verfasser]. "Affine nilTemperley-Lieb algebras and generalized Weyl algebras: Combinatorics and representation theory / Joanna Meinel." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1122193874/34.

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Tarrago, Pierre. "Non-commutative generalization of some probabilistic results from representation theory." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1123/document.

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Le sujet de cette thèse est la généralisation non-commutative de résultats probabilistes venant de la théorie des représentations. Les résultats obtenus se divisent en trois parties distinctes. Dans la première partie de la thèse, le concept de groupe quantique easy est étendu au cas unitaire. Tout d'abord, nous donnons une classification de l'ensemble des groupes quantiques easy unitaires dans le cas libre et classique. Nous étendons ensuite les résultats probabilistes de au cas unitaire. La deuxième partie de la thèse est consacrée à une étude du produit en couronne libre. Dans un premier te
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Charles, Balthazar. "Combinatorics and computations : Cartan matrices of monoids & minimal elements of Shi arrangements." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG063.

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Cette thèse présente le résultat de recherches sur deux thèmes combinatoires distincts: le calcul effectif des matrices de Cartan en théorie des représentations des monoïdes et l'exploration des propriétés des éléments minimaux dans les arrangements de Shi des groupes de Coxeter. Bien que disparates, ces deux domaines de recherche partagent l'utilisation de méthodes combinatoires et d'exploration informatique, soit en tant que fin en soi pour le premier domaine, soit comme aide à la recherche pour le second. Dans la première partie de la thèse, nous développons des méthodes pour le calcul effe
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Books on the topic "Combinatorial representation theory"

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Kang, Seok-Jin, and Kyu-Hwan Lee, eds. Combinatorial and Geometric Representation Theory. American Mathematical Society, 2003. http://dx.doi.org/10.1090/conm/325.

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Kazuhiko, Koike, and Nihon Sūgakkai, eds. Combinatorial methods in representation theory. Published for the Mathematical Society of Japan by Kinokuniya, 2000.

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Japan) Conference "Expansion of Combinatorial Representation Theory" (2007 Kyoto. New trends in combinatorial representation theory. Research Institute for Mathematical Sciences, Kyoto University, 2009.

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Conference "Combinatorial Representation Theory and Related Topics" (2006 Kyoto, Japan). Combinatorial representation theory and related topics. Research Institute for Mathematical Sciences, Kyoto University, 2008.

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Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. Kenkyū Shūkai. Topics in combinatorial representation theory: October 11-14, 2011. Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2012.

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A, Kaimanovich Vadim, and Lodkin A. 1945-, eds. Representation theory, dynamical systems, and asymptotic combinatorics. American Mathematical Society, 2006.

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Seok-Jin, Kang, and Lee Kyu-Hwan 1970-, eds. Combinatorial and geometric representation theory: An international conference on combinatorial and geometric representation theory, October 22-26, 2001, Seoul National University, Seoul, Korea. American Mathematical Society, 2003.

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Chari, Vyjayanthi, Jacob Greenstein, Kailash Misra, K. Raghavan, and Sankaran Viswanath, eds. Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory. American Mathematical Society, 2013. http://dx.doi.org/10.1090/conm/602.

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India) International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory (2010 Bangalore. Recent developments in algebraic and combinatorial aspects of representation theory: International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, August 12-16, 2010, National Institute of Advanced Studies, Bangalore, India : Conference on Algebraic and Combinatorial Approaches to Representation Theory, May 18-20, 2012, University of California, Riverside, CA. Edited by Chari, Vyjayanthi, editor of compilation and Conference on Algebraic and Combinatorial Approaches to Representation Theory (2012 : Riverside, Calif.). American Mathematical Society, 2013.

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1959-, Ariki Susumu, ed. Algebraic groups and quantum groups: International Conference on Representation Theory of Algebraic Groups and Quantum Groups, August 2-6, 2010, Nagoya University, Nagoya, Japan. American Mathematical Society, 2012.

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Book chapters on the topic "Combinatorial representation theory"

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Barot, Michael. "Combinatorial Invariants." In Introduction to the Representation Theory of Algebras. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11475-0_8.

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Kang, Seok-Jin. "Combinatorial Representation Theory and Crystal Bases." In Proceedings of the Third International Algebra Conference. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0337-6_4.

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Brenner, Sheila. "A combinatorial characterisation of finite Auslander-Reiten quivers." In Representation Theory I Finite Dimensional Algebras. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075256.

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Baumslag, Gilbert. "Affine algebraic sets and the representation theory of finitely generated groups." In Topics in Combinatorial Group Theory. Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8587-4_5.

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Lenart, Cristian. "Combinatorial representation theory of Lie algebras. Richard Stanley’s work and the way it was continued." In The Mathematical Legacy of Richard P. Stanley. American Mathematical Society, 2016. http://dx.doi.org/10.1090//mbk/100/15.

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Chen, Yu-Fang, Philipp Rümmer, and Wei-Lun Tsai. "A Theory of Cartesian Arrays (with Applications in Quantum Circuit Verification)." In Automated Deduction – CADE 29. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38499-8_10.

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AbstractWe present a theory of Cartesian arrays, which are multi-dimensional arrays with support for the projection of arrays to sub-arrays, as well as for updating sub-arrays. The resulting logic is an extension of Combinatorial Array Logic (CAL) and is motivated by the analysis of quantum circuits: using projection, we can succinctly encode the semantics of quantum gates as quantifier-free formulas and verify the end-to-end correctness of quantum circuits. Since the logic is expressive enough to represent quantum circuits succinctly, it necessarily has a high complexity; as we show, it suffices to encode the k-color problem of a graph under a succinct circuit representation, an NEXPTIME-complete problem. We present an NEXPTIME decision procedure for the logic and report on preliminary experiments with the analysis of quantum circuits using this decision procedure.
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Rota, Gian-Carlo. "Combinatorics, Representation Theory and Invariant Theory." In Indiscrete Thoughts. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-0-8176-4781-0_3.

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Palmér, Hanna, and Jorryt van Bommel. "Young Students’ Choice of Representation When Solving a Problem-Solving Task on Combinatorics." In Teaching Mathematics as to be Meaningful – Foregrounding Play and Children’s Perspectives. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-37663-4_9.

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AbstractThis paper is about the representations young students use when they are working on a problem-solving task on combinatorics. Results from previous studies on young students and combinatorics have shown connections between the representations used and the extent to which students solved the task. Based on these previous results, young students in this study were interviewed about their choice of representation. In this paper, the rationales expressed by the students are connected to the representation and stage of systematization shown in their documentation. The results indicate that difficulties in representing the context of the problem-solving task may force some of the students to work with a representation on a level of abstraction not suitable for them. Working with representations at an unsuitable level of abstraction may in turn influence how the students manage to complete the problem-solving task.
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Méliot, Pierre-Loïc. "Combinatorics of partitions and tableaux." In Representation Theory of Symmetric Groups. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315371016-4.

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Schnabel, R. "Representation of Graphs by Integers." In Topics in Combinatorics and Graph Theory. Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_73.

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Conference papers on the topic "Combinatorial representation theory"

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Wu, Kaisheng, Liangda Fang, Liping Xiong, et al. "Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/236.

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Strategy representation and reasoning has recently received much attention in artificial intelligence. Impartial combinatorial games (ICGs) are a type of elementary and fundamental games in game theory. One of the challenging problems of ICGs is to construct winning strategies, particularly, generalized winning strategies for possibly infinitely many instances of ICGs. In this paper, we investigate synthesizing generalized winning strategies for ICGs. To this end, we first propose a logical framework to formalize ICGs based on the linear integer arithmetic fragment of numeric part of PDDL. We
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HLINĚNÝ, PETR. "COMBINATORIAL GENERATION OF MATROID REPRESENTATIONS: THEORY AND PRACTICE." In Proceedings of the 3rd Asian Applied Computing Conference. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2007. http://dx.doi.org/10.1142/9781860948534_0001.

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Rumynin, Dmitriy. "Kac-Moody Groups and Their Representations." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0020.

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Sullivan, Eric, Scott Ferguson, and Joseph Donndelinger. "Exploring Differences in Preference Heterogeneity Representation and Their Influence in Product Family Design." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48596.

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When using conjoint studies for market-based design, two model types can be fit to represent the heterogeneity present in a target market, discrete or continuous. In this paper, data from a choice-based conjoint study with 2275 respondents is analyzed for a 19-attribute combinatorial design problem with over 1 billion possible product configurations. Customer preferences are inferred from the choice task data using both representations of heterogeneity. The hierarchical Bayes mixed logit model exemplifies the continuous representation of heterogeneity, while the latent class multinomial logit
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Ahmed, Faez, Yaxin Cui, Yan Fu, and Wei Chen. "A Graph Neural Network Approach for Product Relationship Prediction." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-69462.

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Abstract Graph representation learning has revolutionized many artificial intelligence and machine learning tasks in recent years, ranging from combinatorial optimization, drug discovery, recommendation systems, image classification, social network analysis to natural language understanding. This paper shows their efficacy in modeling relationships between products and making predictions for unseen product networks. By representing products as nodes and their relationships as edges of a graph, we show how an inductive graph neural network approach, named GraphSAGE, can efficiently learn contin
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Klisura, Ðorže. "Embedding Non-planar Graphs: Storage and Representation." In 7th Student Computer Science Research Conference. University of Maribor Press, 2021. http://dx.doi.org/10.18690/978-961-286-516-0.13.

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In this paper, we propose a convention for repre-senting non-planar graphs and their least-crossing embeddings in a canonical way. We achieve this by using state-of-the-art tools such as canonical labelling of graphs, Nauty’s Graph6 string and combinatorial representations for planar graphs. To the best of our knowledge, this has not been done before. Besides, we implement the men-tioned procedure in a SageMath language and compute embeddings for certain classes of cubic, vertex-transitive and general graphs. Our main contribution is an extension of one of the graph data sets hosted on MathDat
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Xu, Jieping, and William T. Rhodes. "State-space representation for multifrequency acoustooptic interactions." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mp1.

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The theory of acoustooptic (AO) interactions can be established from a wave (diffraction) viewpoint or a particle (photon-photon scattering) viewpoint. Recently the theory of Feynman diagrams was used with some success to further develop a scattering-based theory of acoustooptic interactions. We have augmented that approach with a state-space representation of the possible scattering interactions. This state-space representation greatly simplifies the combinatoric problems that must be solved to determine scattering amplitudes (diffraction efficiencies) in various acoustooptic diffraction regi
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Menguy, Grégoire, Sébastien Bardin, Nadjib Lazaar, and Arnaud Gotlieb. "Active Disjunctive Constraint Acquisition." In 20th International Conference on Principles of Knowledge Representation and Reasoning {KR-2023}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/kr.2023/50.

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Constraint acquisition (CA) is a method for learning users' concepts by representing them as a conjunction of constraints. While this approach works well for many combinatorial problems over finite domains, some applications require the acquisition of disjunctive constraints, possibly coming from logical implications or negations. In this paper, we propose the first CA algorithm tailored to the automatic inference of disjunctive constraints, named DCA. A key ingredient there, is to build upon the computation of maximal satisfiable subsets. We demonstrate experimentally that DCA is faster and m
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Luo, Kailun, and Yongmei Liu. "Automatic Verification of FSA Strategies via Counterexample-Guided Local Search for Invariants." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/251.

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Strategy representation and reasoning has received much attention over the past years. In this paper, we consider the representation of general strategies that solve a class of (possibly infinitely many) games with similar structures, and their automatic verification, which is an undecidable problem. We propose to represent a general strategy by an FSA (Finite State Automaton) with edges labelled by restricted Golog programs. We formalize the semantics of FSA strategies in the situation calculus. Then we propose an incomplete method for verifying whether an FSA strategy is a winning strategy b
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Cohen, Jaime, Luiz A. Rodrigues, and Elias P. Duarte Jr. "Improved Parallel Implementations of Gusfield’s Cut Tree Algorithm." In Simpósio em Sistemas Computacionais de Alto Desempenho. Sociedade Brasileira de Computação, 2011. http://dx.doi.org/10.5753/wscad.2011.17275.

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This work presents parallel versions of Gusfield’s cut tree algorithm and the proposal of two heuristics aimed at improving their performance. Cut trees are a compact representation of the edge-connectivity between every pair of vertices of an undirected graph. Cut trees have a vast number of applications in combinatorial optimization and in the analysis of networks originated in many applied fields. However, surprisingly few works have been published on the practical performance of cut tree algorithms. This paper describes two parallel versions of Gusfield’s cut tree algorithm and presents ex
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