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Journal articles on the topic 'Geometrie combinatorie'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

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1

Dress, Andreas W. M., and Walter Wenzel. "Geometric algebra for combinatorial geometries." Advances in Mathematics 77, no. 1 (1989): 1–36. http://dx.doi.org/10.1016/0001-8708(89)90013-3.

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2

Annamalai, Chinnaraji. "Computation and Calculus for Combinatorial Geometric Series and Binomial Identities and Expansions." Journal of Engineering and Exact Sciences 8, no. 7 (2022): 14648–01. http://dx.doi.org/10.18540/jcecvl8iss7pp14648-01i.

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Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial geometric series, and innovative binomial theorems. Combinatorics involves integers, factorials, binomial coefficients, discrete mathematics, and theoretical computer science for finding solutions to the problems in computing and engineerin

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3

Biggs, N. L. "GEOMETRIC ALGORITHMS AND COMBINATORIAL OPTIMIZATION: (Algorithms and Combinatorics 2)." Bulletin of the London Mathematical Society 22, no. 2 (1990): 204–5. http://dx.doi.org/10.1112/blms/22.2.204.

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4

Rau, A. R. P. "Symmetries and Geometries of Qubits, and Their Uses." Symmetry 13, no. 9 (2021): 1732. http://dx.doi.org/10.3390/sym13091732.

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The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such systems for quantum information processes. In the last two decades, two different approaches, with independent starting points and motivations, have been combined for this purpose. One approach has been to develop the unitary time evolution of two or more qubits in order to study quantum correlations; by exploit

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5

Grünbaum, Branko. "Geometric Realization of Some Triangle-Free Combinatorial Configurations." ISRN Geometry 2012 (July 9, 2012): 1–10. http://dx.doi.org/10.5402/2012/560760.

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The main purpose of this paper is to illustrate the mutual benefit to combinatorics and geometry by considering a topic from both sides. Al-Azemi and Betten enumerate the distinct combinatorial (223) configurations that are triangle free. They find a very large number of such configurations, but when taking into account the automorphism group of each, they find two cases in which there is only a single configuration. On the heuristic assumption that an object that is unique in some sense may well have other interesting properties, the geometric counterparts of these configurations were studied

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6

Annamalai, Chinnaraji. "COMBINATORIAL OPTIMIZED TECHNIQUE FOR COMPUTATION OF TRADITIONAL COMBINATIONS." jnanabha 50, no. 02 (2020): 128–31. http://dx.doi.org/10.58250/jnanabha.2020.50215.

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This paper presents a computing method and models for optimizing the combination defined in combinatorics. The optimized combination has been derived from the iterative computation of multiple geometric series and summability by specialized approach. The optimized combinatorial technique has applications in science, engineering and management. In this paper, several properties and consequences on the innovative optimized combination has been introduced that are useful for scientific researchers who are solving scientific problems and meeting today’s challenges.

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7

Abe, Takuro, Graham Denham, Eva Maria Feichtner, and Gerhard Röhrle. "Arrangements, Matroids and Logarithmic Vector Fields." Oberwolfach Reports 21, no. 2 (2024): 1615–76. http://dx.doi.org/10.4171/owr/2024/29.

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The focus of this workshop was on the ongoing interaction between geometric aspects of matroid theory with various directions in the study of hyperplane arrangements. A hyperplane arrangement is exactly a linear realization of a (loop-free, simple) matroid. While a matroid is a purely combinatorial object, though, an arrangement is associated with a range of algebraic and geometric constructions that connect closely with the combinatorics of matroids.The meeting brought together researchers involved with complementary angles on the subject, many of whom had not met before, so an important unde

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8

Annamalai, Chinnaraji, Junzo Watada, Said Broumi, and Vishnu Narayan Mishra. "COMBINATORIAL TECHNIQUE FOR OPTIMIZING THE COMBINATION." Journal of Engineering and Exact Sciences 6, no. 2 (2020): 0189–92. http://dx.doi.org/10.18540/jcecvl6iss2pp0189-0192.

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This paper presents an innovative computing method and models for optimizing the combination defined in combinatorics. The optimized combination has been derived from the iterative computation of multiple geometric series and summability by specialized approach. The optimized combinatorial technique has applications in science, engineering and management. In this paper, several properties and consequences on the innovative optimized combination has been introduced that are useful for scientific researchers who are solving scientific problems and meeting today’s challenges.

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9

CAVİCCHİOLİ, Alberto, and Fulvia SPAGGİARİ. "All Dehn Fillings of the Whitehead Link Complement are Tetrahedron Manifolds." International Electronic Journal of Geometry 15, no. 2 (2022): 192–201. http://dx.doi.org/10.36890/iejg.1102753.

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In this paper we show that Dehn surgeries on the oriented components of the Whitehead link yield tetrahedron manifolds of Heegaard genus $\le 2$. As a consequence, the eight homogeneous Thurston 3-geometries are realized by tetrahedron manifolds of Heegaard genus $\le 2$. The proof is based on techniques of Combinatorial Group Theory, and geometric presentations of manifold fundamental groups.

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10

Kuijken, Elisabeth. "A Geometric Construction of Partial Geometries with a Hermitian Point Graph." European Journal of Combinatorics 23, no. 6 (2002): 701–6. http://dx.doi.org/10.1006/eujc.2002.0558.

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11

Kalai, Gil, Isabella Novik, Francisco Santos, and Volkmar Welker. "Geometric and Algebraic Combinatorics." Oberwolfach Reports 12, no. 1 (2015): 285–368. http://dx.doi.org/10.4171/owr/2015/5.

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12

Wilson, B. J. "COMBINATORICS OF FINITE GEOMETRIES." Bulletin of the London Mathematical Society 19, no. 1 (1987): 85–86. http://dx.doi.org/10.1112/blms/19.1.85.

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13

Halsey, Mark D. "Line-closed combinatorial geometries." Discrete Mathematics 65, no. 3 (1987): 245–48. http://dx.doi.org/10.1016/0012-365x(87)90056-2.

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14

van Dam, Edwin R., and Willem H. Haemers. "Geometric and algebraic combinatorics." European Journal of Combinatorics 28, no. 7 (2007): 1877. http://dx.doi.org/10.1016/j.ejc.2006.08.001.

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15

Vergès, Matthieu Josuat. "Cumulants of the q-semicircular Law, Tutte Polynomials, and Heaps." Canadian Journal of Mathematics 65, no. 4 (2013): 863–78. http://dx.doi.org/10.4153/cjm-2012-042-9.

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AbstractThe q-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of itsmoments in terms ofmatchings, where q follows the number of crossings, whereas for the free cumulants one has to restrict the enumeration to connected matchings. The purpose of this article is to describe combinatorial properties of the classical cumulants. We show that like the free cumulants, they are obtained by an enumeration of connected matchings, the weight being now an evaluation of the Tutte polynomial of a so-c

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16

LI, NAN, and AMOS RON. "EXTERNAL ZONOTOPAL ALGEBRA." Journal of Algebra and Its Applications 13, no. 02 (2013): 1350097. http://dx.doi.org/10.1142/s0219498813500977.

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Zonotopal algebra studies pairs of dual algebraic structures that are associated with a linear matroid X and are connected to corresponding dual geometries. Both the geometry and the algebra encode in their statistics combinatorial properties of the matroid. We provide in this paper a general, unified, framework for the chapter in zonotopal algebra that is known as external. The approach is critically based on employing simultaneously the two dual algebraic constructs and invokes the underlying matroidal and geometric structures in an essential way.

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17

Stokes, Klara, and Milagros Izquierdo. "Geometric point-circle pentagonal geometries from Moore graphs." Ars Mathematica Contemporanea 11, no. 1 (2015): 215–29. http://dx.doi.org/10.26493/1855-3974.787.925.

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18

Annamalai, Chinnaraji, and Antonio Marcos de Oliveira Siqueira. "Skew Field on the Binomial Coefficients in Combinatorial Geometric Series." Journal of Engineering and Exact Sciences 8, no. 11 (2022): 14859–01. http://dx.doi.org/10.18540/jcecvl8iss11pp14859-01i.

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This paper discusses a commutative group, ring, and field under addition and multiplication of the binomial coefficients in combinatorial geometric series. The combinatorial geometric series is derived from the multiple summations of geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. This idea can enable the scientific researchers to solve the real life problems.

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19

Annamalai, Chinnaraji, and Antonio Marcos de Oliveira Siqueira. "Abelian Group on the Binomial Coefficients in Combinatorial Geometric Series." Journal of Engineering and Exact Sciences 8, no. 10 (2022): 14799–01. http://dx.doi.org/10.18540/jcecvl8iss10pp14799-01i.

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This paper discusses an abelian group, also called a commutative group, under addition of the binomial coefficients of combinatorial geometric series. The combinatorial geometric series is derived from the multiple summations of geometric series The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. This idea can enable the scientific researchers to solve the real life problems.

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20

Moraglio, Alberto, Cecilia Di Chio, Julian Togelius, and Riccardo Poli. "Geometric Particle Swarm Optimization." Journal of Artificial Evolution and Applications 2008 (February 21, 2008): 1–14. http://dx.doi.org/10.1155/2008/143624.

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Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new Geometric PSO (GPSO) applies naturally to both continuous and combinatorial spaces. We demonstrate this for the cases of Euclidean, Manhattan and Hamming spaces and report extensive experimental results. We also demonstrate the applicability of GPSO to more challenging combinat

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21

Chakerian, Don, Vladimir Boltyanski, and Alexander Soifer. "Geometric Etudes in Combinatorial Mathematics." American Mathematical Monthly 99, no. 5 (1992): 486. http://dx.doi.org/10.2307/2325111.

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22

Leung, Janny, Martin Grotschel, Laszlo Lovasz, and Alexander Schrijver. "Geometric Algorithms and Combinatorial Optimization." Journal of the Operational Research Society 40, no. 8 (1989): 797. http://dx.doi.org/10.2307/2583689.

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23

Gardiner, Tony, V. Boltyanski, and A. Soifer. "Geometric Studies in Combinatorial Mathematics." Mathematical Gazette 76, no. 476 (1992): 320. http://dx.doi.org/10.2307/3619184.

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24

Kalai, Gil, Isabella Novik, Francisco Santos, and Volkmar Welker. "Geometric, Algebraic, and Topological Combinatorics." Oberwolfach Reports 16, no. 3 (2020): 2395–472. http://dx.doi.org/10.4171/owr/2019/39.

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25

Adiprasito, Karim, June Huh, and Eric Katz. "Hodge theory for combinatorial geometries." Annals of Mathematics 188, no. 2 (2018): 381–452. http://dx.doi.org/10.4007/annals.2018.188.2.1.

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26

Gismatullin, Jakub. "Combinatorial geometries of field extensions." Bulletin of the London Mathematical Society 40, no. 5 (2008): 789–800. http://dx.doi.org/10.1112/blms/bdn057.

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27

Kalai, Gil, Isabella Novik, Francisco Santos, and Volkmar Welker. "Geometric, Algebraic and Topological Combinatorics." Oberwolfach Reports 20, no. 4 (2024): 3249–318. http://dx.doi.org/10.4171/owr/2023/58.

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28

Leung, Janny. "Geometric Algorithms and Combinatorial Optimization." Journal of the Operational Research Society 40, no. 8 (1989): 797. http://dx.doi.org/10.1057/jors.1989.134.

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29

Osetinskii, N. I., O. O. Vasil’ev, and F. S. Vainstein. "Geometric combinatorics of Kalman algebras." Differential Equations 42, no. 11 (2006): 1604–11. http://dx.doi.org/10.1134/s0012266106110103.

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30

Teng, Shang-Hua. "Combinatorial aspects of geometric graphs." Computational Geometry 9, no. 4 (1998): 277–87. http://dx.doi.org/10.1016/s0925-7721(96)00008-9.

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31

Rota, Gian-Carlo. "Geometric algorithms and combinatorial optimization." Advances in Mathematics 82, no. 2 (1990): 267. http://dx.doi.org/10.1016/0001-8708(90)90093-3.

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32

Lee, Jon, and Walter D. Morris. "Geometric comparison of combinatorial polytopes." Discrete Applied Mathematics 55, no. 2 (1994): 163–82. http://dx.doi.org/10.1016/0166-218x(94)90006-x.

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33

van Dam, Edwin R., and Willem H. Haemers. "Preface: Geometric and algebraic combinatorics." Designs, Codes and Cryptography 65, no. 1-2 (2012): 1–3. http://dx.doi.org/10.1007/s10623-012-9701-7.

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34

Kamnitzer, Joel. "A combinatorial geometric Satake equivalence." Advances in Mathematics 300 (September 2016): 5–16. http://dx.doi.org/10.1016/j.aim.2016.03.014.

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35

Heckenberger, István, and Volkmar Welker. "Geometric combinatorics of Weyl groupoids." Journal of Algebraic Combinatorics 34, no. 1 (2010): 115–39. http://dx.doi.org/10.1007/s10801-010-0264-2.

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36

Chen, Hao, and Jean-Marc Schlenker. "Weakly inscribed polyhedra." Transactions of the American Mathematical Society, Series B 9, no. 14 (2022): 415–49. http://dx.doi.org/10.1090/btran/59.

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Motivated by an old question of Steiner, we study convex polyhedra in R P 3 \mathbb {R}\mathrm {P}^3 with all their vertices on a sphere, but the polyhedra themselves do not lie on one side the sphere. We give an explicit combinatorial description of the possible combinatorics of such polyhedra. The proof uses a natural extension of the 3-dimensional hyperbolic space by the de Sitter space. Polyhedra with their vertices on the sphere are interpreted as ideal polyhedra in this extended space. We characterize the possible dihedral angles of those ideal polyhedra, as well as the geometric structu

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37

Billey, Sara, and Jordan Weaver. "Criteria for smoothness of positroid varieties via pattern avoidance, Johnson graphs, and spirographs." Transactions of the American Mathematical Society, Series B 12, no. 4 (2025): 112–64. https://doi.org/10.1090/btran/190.

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Positroids are certain representable matroids originally studied by Postnikov in connection with the totally nonnegative Grassmannian and now used widely in algebraic combinatorics. The positroids give rise to determinantal equations defining positroid varieties as subvarieties of the Grassmannian variety. Rietsch, Knutson-Lam-Speyer, and Pawlowski studied geometric and cohomological properties of these varieties. In this paper, we continue the study of the geometric properties of positroid varieties by establishing several equivalent conditions characterizing smooth positroid varieties using

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38

Kus, Deniz, and Bea Schumann. "Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers." Algebra and Discrete Mathematics 34, no. 2 (2022): 244–72. http://dx.doi.org/10.12958/adm1952.

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We obtain an explicit crystal isomorphism between two realizations of crystal bases of finite dimensional irreducible representations of simple Lie algebras of type A and D. The first realization we consider is a geometric construction in terms of irreducible components of certain Nakajima quiver varieties established by Saito and the second is a realization in terms of isomorphism classes of quiver representations obtained by Reineke. We give a homological description of the irreducible components of Lusztig's quiver varieties which correspond to the crystal of a finite dimensional representa

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39

MICHELUCCI, DOMINIQUE, and PASCAL SCHRECK. "INCIDENCE CONSTRAINTS: A COMBINATORIAL APPROACH." International Journal of Computational Geometry & Applications 16, no. 05n06 (2006): 443–60. http://dx.doi.org/10.1142/s0218195906002130.

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The simplest geometric constraints are incidences between points and lines in the projective plane. This problem is universal, in the sense that all algebraic systems reduce to such geometric constraints. Detecting incidence dependences between these geometric constraints is NP-complete. New methods to prove incidence theorems are proposed, which use strictly no computer algebra but only combinatorial arguments.

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40

Alyabieva, Valentina. "From the History of Combinatorial Analysis: From Idea to Research Schools." Вестник Пермского университета. Математика. Механика. Информатика, no. 2(57) (2022): 14–25. http://dx.doi.org/10.17072/1993-0550-2022-2-14-25.

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The article explores the development of combinatorial analysis from the idea to scientific schools. Combinatorial research was stimulated by G.W. Leibniz's ideas about combinatorial art and special geometric analysis – Analysis Situs in the 17th century. Various combinatorial problems were solved by L. Euler in the XVIII century. The first scientific school of combinatorial analysis arose by K.F. Hindenburg in the second half of the 18th century in Germany. Combinatorial-geometric configurations were studied in the 19th century. A. Cayley and J. Sylvester coined the term tactics for a special

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41

Annamalai, Chinnaraji, and Antonio Marcos de Oliveira Siqueira. "Vector Space on the Binomial Coefficients in Combinatorial Geometric Series." Journal of Engineering and Exact Sciences 9, no. 6 (2023): 15413–01. http://dx.doi.org/10.18540/jcecvl9iss6pp15413-01e.

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A vector space is a group of objects that is closed under finite vector addition and scalar multiplication. This paper discusses a vector space under addition and multiplication of binomial coefficients defined in combinatorial geometric series. The combinatorial geometric series is a geometric series with binomial coefficients that is derived from the multiple summations of geometric series. This idea can enable the scientific researchers to solve the real world problems.

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42

Precup, Martha, and Edward Richmond. "An equivariant basis for the cohomology of Springer fibers." Transactions of the American Mathematical Society, Series B 8, no. 17 (2021): 481–509. http://dx.doi.org/10.1090/btran/57.

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Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant cohomology of Springer fibers for G L n ( C ) GL_n(\mathbb {C}) using results of Kumar and Procesi that describe this equivariant cohomology as a quotient ring. We define a basis for the equivariant cohomology of a Springer fiber, generalizing a monomial basis of the ordinary cohomology defined by De Concini and Procesi and studied by Garsia and Procesi. Our construction yields a combinatorial framework with which to st

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43

Breuillard, Emmanuel, Amador Martin-Pizarro, Katrin Tent, and Frank Olaf Wagner. "Model Theory: Groups, Geometries and Combinatorics." Oberwolfach Reports 17, no. 1 (2021): 91–142. http://dx.doi.org/10.4171/owr/2020/2.

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44

Halsey, Mark D. "Extensions of line-closed combinatorial geometries." Discrete Mathematics 82, no. 3 (1990): 259–62. http://dx.doi.org/10.1016/0012-365x(90)90203-t.

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45

Beutelspacher, Albrecht. "A combinatorial characterization of geometric spreads." Discrete Mathematics 97, no. 1-3 (1991): 59–62. http://dx.doi.org/10.1016/0012-365x(91)90421-w.

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46

Petronio, Carlo, Damian Heard, and Ekaterina Pervova. "Combinatorial and Geometric Methods in Topology." Milan Journal of Mathematics 76, no. 1 (2007): 69–92. http://dx.doi.org/10.1007/s00032-007-0080-x.

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47

Shanmugam, Ramalingam. "Combinatorial inference in geometric data analysis." Journal of Statistical Computation and Simulation 89, no. 18 (2019): 3497–98. http://dx.doi.org/10.1080/00949655.2019.1628887.

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48

Abdullah; YILDIZ, PAŞA. "Constructing Gray maps from combinatorial geometries." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 63, no. 2 (2014): 147–61. http://dx.doi.org/10.1501/commua1_0000000720.

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49

Veilande, Ingrida. "Solving methods of combinatorial geometric problems." ZDM 38, no. 6 (2006): 488–97. http://dx.doi.org/10.1007/bf02652786.

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50

Forcey, S., and Derriell Springfield. "Geometric combinatorial algebras: cyclohedron and simplex." Journal of Algebraic Combinatorics 32, no. 4 (2010): 597–627. http://dx.doi.org/10.1007/s10801-010-0229-5.

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