콕세터 군에서의 축약 표현

수학노트
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메모

  • It is an old result of Stanley that the number of reduced words for the longest permutation in Sn is the dimension of the irreducible representation of the symmetric group indexed by the staircase shape partition \(\delta_=(n−1,n−2,…,2,1)\)
  • Involution words are certain analogues of reduced words for involutions in Coxeter groups, first studied under the name of "admissible sequences" by Richardson and Springer.


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관련논문

  • Hamaker, Zachary, Eric Marberg, and Brendan Pawlowski. “Involution Words: Counting Problems and Connections to Schubert Calculus for Symmetric Orbit Closures.” arXiv:1508.01823 [math], August 7, 2015. http://arxiv.org/abs/1508.01823.
  • Shi, Jian-yi. "The reduced expressions in a Coxeter system with a strictly complete Coxeter graph." Advances in Mathematics 272 (2015): 579-597.
  • Denoncourt, Hugh. “Some Combinatorial Models for Reduced Expressions in Coxeter Groups.” arXiv:1104.3533 [math], April 18, 2011. http://arxiv.org/abs/1104.3533.
  • Stembridge, John. “Some Combinatorial Aspects of Reduced Words in Finite Coxeter Groups.” Transactions of the American Mathematical Society 349, no. 4 (1997): 1285–1332. doi:10.1090/S0002-9947-97-01805-9.
  • Winkel, Rudolf. “Schubert Functions and the Number of Reduced Words of Permutations.” Séminaire Lotharingien de Combinatoire [electronic Only] 39 (1997). https://eudml.org/doc/119309.
  • Eriksson, Kimmo. “Reduced Words in Affine Coxeter Groups.” Discrete Mathematics 157, no. 1–3 (October 1, 1996): 127–46. doi:10.1016/S0012-365X(96)83011-1.
  • Winkel, Rudolf. "A combinatorial bijection between standard Young tableaux and reduced words of Grassmannian permutations." Seminaire Lotharingien et Combinatoire, B36h (1996).
  • Brink, Brigitte, and Robert B. Howlett. “A Finiteness Property an an Automatic Structure for Coxeter Groups.” Mathematische Annalen 296, no. 1 (December 1993): 179–90. doi:10.1007/BF01445101.
  • Stanley, Richard P. “On the Number of Reduced Decompositions of Elements of Coxeter Groups.” European Journal of Combinatorics 5, no. 4 (December 1984): 359–72. doi:10.1016/S0195-6698(84)80039-6.
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