Relevant bibliographies by topics / Representation of the symmetric group

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Representation of the symmetric group'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Representation of the symmetric group"

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Lewis, Joel Brewster. "Affine symmetric group." WikiJournal of Science 4, no. 1 (2021): 3. http://dx.doi.org/10.15347/wjs/2021.003.

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The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tesselation of the plane, as well as related higher dimensional objects. It is an infinite extension of the symmetric group, which consists of all permutations (rearrangements) of a finite set. In additition to its geometric description, the affine symmetric group may be defined as the collection of permutations of the integers (..., −2, −1, 0, 1, 2, ...) that are periodic in a certain sense, or in purely algebraic terms as a group with certain generators and relations. These different definitions allow for the extension of many important properties of the finite symmetric group to the infinite setting, and are studied as part of the fields of combinatorics and representation theory.
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Dresselhaus, M. S., and G. Dresselhaus. "Note on sufficient symmetry conditions for isotropy of the elastic moduli tensor." Journal of Materials Research 6, no. 5 (1991): 1114–18. http://dx.doi.org/10.1557/jmr.1991.1114.

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Group theoretical methods are used to obtain the form of the elastic moduli matrices and the number of independent parameters for various symmetries. Particular attention is given to symmetry groups for which 3D and 2D isotropy is found for the stress-strain tensor relation. The number of independent parameters is given by the number of times the fully symmetric representation is contained in the direct product of the irreducible representations for two symmetrical second rank tensors. The basis functions for the lower symmetry groups are found from the compatibility relations and are explicitly related to the elastic moduli. These types of symmetry arguments should be generally useful in treating the elastic properties of solids and composites.
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Obata, Nobuaki. "Certain Unitary Representations of the Infinite Symmetric Group, I." Nagoya Mathematical Journal 105 (March 1987): 121–28. http://dx.doi.org/10.1017/s0027763000000775.

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Let X be the set of all natural numbers and let be the group of all finite permutations of X. The group equipped with the discrete topology, is called the infinite symmetric group. It was discussed in F. J. Murray and J. von Neumann as a concrete example of an ICC-group, which is a discrete group with infinite conjugacy classes. It is proved that the regular representation of an ICC-group is a factor representation of type II1. The infinite symmetric group is, therefore, a group not of type I. This may be the reason why its unitary representations have not been investigated satisfactorily. In fact, only few results are known. For instance, all indecomposable central positive definite functions on , which are related to factor representations of type IIl, were given by E. Thoma. Later on, A. M. Vershik and S. V. Kerov obtained the same result by a different method in and gave a realization of the representations of type II1 in. Concerning irreducible representations, A. Lieberman and G. I. Ol’shanskii obtained a characterization of a certain family of countably many irreducible representations by introducing a particular topology in However, irreducible representations have been studied not so actively as factor representations.
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Daugherty, Zajj, Alexander K. Eustis, Gregory Minton, and Michael E. Orrison. "Voting, the Symmetric Group, and Representation Theory." American Mathematical Monthly 116, no. 8 (2009): 667–87. http://dx.doi.org/10.4169/193009709x460796.

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RAUHUT, HOLGER. "WAVELET TRANSFORMS ASSOCIATED TO GROUP REPRESENTATIONS AND FUNCTIONS INVARIANT UNDER SYMMETRY GROUPS." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 02 (2005): 167–87. http://dx.doi.org/10.1142/s0219691305000816.

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We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on ℝd.
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Tsohantjis, I., and M. D. Gould. "Quantum double finite group algebras and link polynomials." Bulletin of the Australian Mathematical Society 49, no. 2 (1994): 177–204. http://dx.doi.org/10.1017/s0004972700016270.

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Unitary representations of the braid group and corresponding link polynomials are constructed corresponding to each irreducible representation of a quantum double finite group algebra. Moreover the diagonal form of the braid generator is derived from which a general closed formula is obtained for link polynomials. As an example, link polynomials corresponding to certain induced representations of the symmetric group and its subgroups are determined explicitly.
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Adve, Anshul, and Alexander Yong. "Symmetric group representations andZ." Comptes Rendus Mathematique 356, no. 1 (2018): 1–4. http://dx.doi.org/10.1016/j.crma.2017.11.009.

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Fiziev, Plamen. "Novel Representation of the General Fuchsian and Heun Equations and their Solutions." International Frontier Science Letters 7 (March 2016): 11–24. http://dx.doi.org/10.18052/www.scipress.com/ifsl.7.11.

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In the present article we introduce and study a novel type of solutions to the general Heun's equation. Our approach is based on the symmetric form of the Heun's differential equation yielded by development of the Papperitz-Klein symmetric form of the Fuchsian equations with an arbitrary number N≥4 of regular singular points. We derive the symmetry group of these equations which turns to be a proper extension of the Mobius group. We also introduce and study new series solutions of the proposed in the present paper symmetric form of the general Heun's differential equation (N=4) which treats simultaneously and on an equal footing all singular points.
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Marin, Ivan. "Hooks generate the representation ring of the symmetric group." Expositiones Mathematicae 30, no. 3 (2012): 268–76. http://dx.doi.org/10.1016/j.exmath.2012.03.005.

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Kempf, Achim. "Quantum group-symmetric fock spaces with bargmann-fock representation." Letters in Mathematical Physics 26, no. 1 (1992): 1–12. http://dx.doi.org/10.1007/bf00420513.

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Dissertations / Theses on the topic "Representation of the symmetric group"

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George, Timothy Edward. "Symmetric representation of elements of finite groups." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3105.

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The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.
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Kangwai, Riki Dale. "The analysis of symmetric structures using group representation theory." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/265422.

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Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any symmetric structure. Group Representation Theory methods currently exist for the Stiffness Niethod of structural analysis, where the stiffness matrix of a structure is block-diagonalised into a number of independent submatrices, each of which relates applied loads and displacements with a particular type of symmetry. This dissertation extends the application of Group Representation Theory to the equilibrium and compatibility matrices which are commonly used in the Force Method of structural analysis. Group Representation Theory is used to find symmetry-adapted coordinate systems for both the external vector space which is suitable for representing the loads applied to a structure, and the internal vector space wh",t-k is-suitable for representing the internal forces. Using these symmetry-adapted coordinate systems the equilibrium matrix is block-diagonalised into a number of independent submatrix blocks, thus decomposing the analysis into a number of subproblems which require less computational effort. Each independent equilibrium submatrix block relates applied loads and internal forces with particular symmetry properties, and hence any states of self-stress or inextensional mechanisms in one of these equilibrium submatrix blocks will necessarily have ~rresponding symmetry properties. Thus, a symmetry analysis provides valuable insight into the behaviour of symmetric structures by helping to identify and classif:)'. any states of self-stress .or inextensional mechanisms present in a structure. In certain cases it is also possible for a symmetry analysis to identify when a structure contains a :ijnite rather than infinitesimal mechanism. To do this a symmetry analysis must b~ carried out using the symmetry properties of the inextensional mechanism of interest. If the analysis shows that any states of self-stress which exist in the structure have "lesser" symmetry properties, then the states of self-stress exist independently from the mechanism and cannot prevent its finite motion.
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Norton, Elizabeth. "Representations and the Symmetric Group." Scholarship @ Claremont, 2002. https://scholarship.claremont.edu/hmc_theses/139.

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The regular representation of the symmetric group Sn is a vector space of dimension n! with many interesting invariant subspaces. The projections of a vector onto these subspaces may be computed by first considering projections onto certain basis elements in the subspace and then recombining later. If all of these projections are kept, it creates an explosion in the size of the data, making it difficult to store and work with. This is a study of techniques to compress this computed data such that it is of the same dimmension as the original vector.
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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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Banister, Melissa. "Separating Sets for the Alternating and Dihedral Groups." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/158.

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This thesis presents the results of an investigation into the representation theory of the alternating and dihedral groups and explores how their irreducible representations can be distinguished with the use of class sums.
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Russell, Lee. "Modular representations of the symmetric group." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627178.

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Scopes, Joanna. "Representations of the symmetric groups." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279989.

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Manriquez, Adam. "Symmetric Presentations, Representations, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/711.

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The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 24 : A5, 34 : S5, PSL(2,31), PSL(2,11), PSL(2,19), PSL(2,41), A8, 34 : S5, A52, 2• A52, 2 : A62, PSL(2,49), 28 : A5, PGL(2,19), PSL(2,71), 24 : A5, 24 : A6, PSL(2,7), 3 x PSL(3,4), 2• PSL(3,4), PSL(3,4), 2• (M12 : 2), 37:S7, 35 : S5, S6, 25 : S6, 35 : S6, 25 : S5, 24 : S6, and M12 as homomorphic images of the permutation progenitors 2*60 : (2 x A5), 2*60 : A5, 2*21 : (7: 3), 2*60 : (2 x A5), 2*120 : S5, and 2*144 : (32 : 24). We have given original proof of the 2*n Symmetric Presentation Theorem. In addition, we have also provided original proof for the Extension of the Factoring Lemma (involutory and non-involutory progenitors). We have constructed S5, PSL(2,7), and U(3,5):2 using the technique of double coset enumeration and by way of linear fractional mappings. Furthermore, we have given proofs of isomorphism types for 7 x 22, U(3,5):2, 2•(M12 : 2), and (4 x 2) :• 22.
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Harris, Elena Yavorska. "Symmetric representation of elements of sporadic groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2844.

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Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.
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Vercheval, Nicolas. "The Representation of Symmetric Groups in Two-Dimensional Persistent Homology." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13545/.

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The two dimensional persistent homology, that can be reduced to the homology of a family of parameterized real functions, can be found to have some issues due to a phenomenon of monodromy, which happens when a loop in the parameters' space doesn't translate into loops of the elements of the persistent diagram. Instead they switch place between them in a functorial way. In this paper we present a formalisation of this functor and we will make an use of it, representing an arbitrary symmetric group by means of a suitable filtering function.
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Books on the topic "Representation of the symmetric group"

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Sagan, Bruce Eli. The symmetric group: Representations, combinatorial algorithms, and symmetric functions. 2nd ed. Springer, 2001.

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Sagan, Bruce Eli. The symmetric group: Representations, combinatorial algorithms, and symmetric functions. Springer, 2000.

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The symmetric group: Representations, combinatorial algorithms, and symmetric functions. Wadsworth & Brooks/Cole Advanced Books & Software, 1991.

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Symmetric and G-algebras: With applications to group representations. Kluwer Academic Publishers, 1990.

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Asymptotic representation theory of the symmetric group and its applications in analysis. American Mathematical Society, 2003.

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Linear and projective representations of symmetric groups. Cambridge University Press, 2005.

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Goldschmidt, David M. Group characters, symmetric functions, and the Hecke algebra. American Mathematical Society, 1993.

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Goldschmidt, David M. Group characters, symmetric functions, and the Hecke algebras. American Mathematical Society, 1993.

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Iwahori-Hecke algebras and Schur algebras of the symmetric group. American Mathematical Society, 1999.

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Fabio, Scarabotti, and Tolli Filippo 1968-, eds. Representation theory of the symmetric groups: The Okounkov-Vershik approach, character formulas, and partition algebras. Cambridge University Press, 2010.

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Book chapters on the topic "Representation of the symmetric group"

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Sobczyk, Garret. "Representation of the Symmetric Group." In New Foundations in Mathematics. Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8385-6_12.

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Méliot, Pierre-Loïc. "Representations of the infinite symmetric group." In Representation Theory of Symmetric Groups. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315371016-15.

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Steinberg, Benjamin. "Representation Theory of the Symmetric Group." In Representation Theory of Finite Groups. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0776-8_10.

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Lakshmibai, V., and Justin Brown. "Representation Theory of the Symmetric Group." In Texts and Readings in Mathematics. Hindustan Book Agency, 2009. http://dx.doi.org/10.1007/978-93-86279-41-5_4.

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Lakshmibai, V., and Justin Brown. "Representation Theory of the Symmetric Group." In Texts and Readings in Mathematics. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1393-6_4.

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Vilenkin, N. Ja, and A. U. Klimyk. "Symmetric Polynomials and Symmetric Functions." In Representation of Lie Groups and Special Functions. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-017-2885-0_2.

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Hassani, Sadri. "Representations of the Symmetric Group." In Mathematical Physics. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01195-0_25.

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Rao, K. N. Srinivasa. "Representations of the Symmetric Group." In Texts and Readings in Physical Sciences. Hindustan Book Agency, 2006. http://dx.doi.org/10.1007/978-93-86279-32-3_7.

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Sagan, Bruce E. "Representations of the Symmetric Group." In Graduate Texts in Mathematics. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-6804-6_2.

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Méliot, Pierre-Loïc. "Symmetric groups and free probability." In Representation Theory of Symmetric Groups. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315371016-12.

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Conference papers on the topic "Representation of the symmetric group"

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LASCOUX, ALAIN. "YOUNGS'S REPRESENTATIONS OF THE SYMMETRIC GROUP." In Proceedings of the Sixth's International School of Theoretical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811479_0010.

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Happawana, G. S., O. D. I. Nwokah, and A. K. Bajaj. "On the Dynamics of Perturbed Symmetric Systems." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0210.

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Abstract In this work, we consider the dynamics of linear mechanical systems possessing geometrical symmetry subject to differential or small parameter variations. The machinery of group theory including the irreducible group representations, and the consideration of representations to which the translational, rotational and vibrational modes belong, allow us to predict apriori, the number and the order of degenerate eigenvalues in the symmetric system. By considering the resultant Hamiltonians of the perturbed symmetric system, we show further the effects of the perturbations on the eigenvalues and their degeneracies. Since the vibration modes of systems with degenerate eigenvalues are known to display sensitive dependence on parameters, we may use these techniques to identify in principle the possibility of maximum vibration amplitudes and where they are likely to occur. Applications of these ideas include the mistimed turbine rotor bladed disk assemblies.
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AYALA-SÁNCHEZ, MAURICIO, and RICHARD W. HAASE. "GROUP CONTRACTIONS AND ITS CONSEQUENCES UPON REPRESENTATIONS OF DIFFERENT SPATIAL SYMMETRY GROUPS." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705068_0008.

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Valderrama-Rodríguez, Juan Ignacio, José M. Rico, J. Jesús Cervantes-Sánchez, and Fernando Tomás Pérez-Zamudio. "A New Look to the Three Axes Theorem." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97443.

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Abstract This paper analyzes the well known three axes theorem under the light of the Lie algebra se(3) of the Euclidean group, SE(3) and the symmetric bilinear forms that can be defined in this algebra. After a brief historical review of the Aronhold-Kennedy theorem and its spatial generalization, the main hypothesis is that the general version of the Aronhold-Kennedy theorem is basically the application of the Killing and Klein forms to the equation that relates the velocity states of three bodies regardless if they are free to move in the space, independent of each other, or they form part of a kinematic chain. Two representative examples are employed to illustrate the hypothesis, one where the rigid bodies are free to move in the space without any connections among them and other concerning a RCCC spatial mechanism.
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Egorova, Elena. "Symmetric group testing with noise." In 2019 XVI International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY). IEEE, 2019. http://dx.doi.org/10.1109/redundancy48165.2019.9003325.

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Ningbo Zhu, Lei Wei, and Ting Xu. "Group representation-based classification." In 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2015. http://dx.doi.org/10.1109/fskd.2015.7382039.

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Hraiz, Safaa, and Wael Etaiwi. "Symmetric encryption algorithm using graph representation." In 2017 8th International Conference on Information Technology (ICIT). IEEE, 2017. http://dx.doi.org/10.1109/icitech.2017.8080049.

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Negrinho, Renato M. P., and Pedro M. Q. Aguiar. "Symmetric polynomials for 2D shape representation." In 2014 IEEE International Conference on Image Processing (ICIP). IEEE, 2014. http://dx.doi.org/10.1109/icip.2014.7025959.

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Emad, Amin, Jun Shen, and Olgica Milenkovic. "Symmetric group testing and superimposed codes." In 2011 IEEE Information Theory Workshop (ITW). IEEE, 2011. http://dx.doi.org/10.1109/itw.2011.6089379.

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Venkatesan, R., E. Nandakumar, and Gaverchand K. "Cellularity of signed symmetric group algebras." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2020. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0025270.

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Reports on the topic "Representation of the symmetric group"

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Valverde, L., and S. V. Ovchinnikov. Representation of Fuzzy Symmetric Relations. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada604022.

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Harries-Jenkins, Gwyn. Group Representation in European Armed Forces. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada298618.

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Pease, R. A., and Todd M. Carrico. Object Model Working Group Core Plan Representation. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada381216.

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Mekjian, A. Z., and S. J. Lee. Models of fragmentation phenomena based on the symmetric group S{sub n} and combinational analysis. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/10107058.

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Mekjian, A. Z., and S. J. Lee. Models of fragmentation phenomena based on the symmetric group S sub n and combinational analysis. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/6091012.

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Blaze, Matt, Whitfield Diffie, Ronald L. Rivest, Bruce Schneier, and Tsutomu Shimomura. Minimal Key Lengths for Symmetric Ciphers to Provide Adequate Commercial Security. A Report by an Ad Hoc Group of Cryptographers and Computer Scientists. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada385264.

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Kindt, Roeland, Ian K Dawson, Jens-Peter B Lillesø, Alice Muchugi, Fabio Pedercini, and James M Roshetko. The one hundred tree species prioritized for planting in the tropics and subtropics as indicated by database mining. World Agroforestry, 2021. http://dx.doi.org/10.5716/wp21001.pdf.

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A systematic approach to tree planting and management globally is hindered by the limited synthesis of information sources on tree uses and species priorities. To help address this, the authors ‘mined’ information from 23 online global and regional databases to assemble a list of the most frequent tree species deemed useful for planting according to database mentions, with a focus on tropical regions. Using a simple vote count approach for ranking species, we obtained a shortlist of 100 trees mentioned in at least 10 of our data sources (the ‘top-100’ species). A longer list of 830 trees that were mentioned at least five times was also compiled. Our ‘top-100’ list indicated that the family Fabaceae (syn. Leguminosae) was most common. The information associated with our mined data sources indicated that the ‘top-100’ list consisted of a complementary group of species of differing uses. These included the following: for wood (mostly for timber) and fuel production, human nutrition, animal fodder supply, and environmental service provision (varied services). Of these uses, wood was most frequently specified, with fuel and food use also highly important. Many of the ‘top-100’ species were assigned multiple uses. The majority of the ‘top-100’ species had weediness characteristics according to ‘attribute’ invasiveness databases that were also reviewed, thereby demonstrating potential environmental concerns associated with tree planting that need to be balanced against environmental and livelihood benefits. Less than half of the ‘top-100’ species were included in the OECD Scheme for the Certification of Forest Reproductive Material, thus supporting a view that lack of germplasm access is a common concern for trees. A comparison of the ‘top-100’ species with regionally-defined tree inventories indicated their diverse continental origins, as would be anticipated from a global analysis. However, compared to baseline expectations, some geographic regions were better represented than others. Our analysis assists in priority-setting for research and serves as a guide to practical tree planting initiatives. We stress that this ‘top-100’ list does not necessarily represent tree priorities for the future, but provides a starting point for also addressing representation gaps. Indeed, our primary concern going forward is with the latter.
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