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Kevin Dilks ; T. Kyle Petersen ; John R. Stembridge - Affine descents and the Steinberg torus

dmtcs:3631 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3631
Affine descents and the Steinberg torusConference paper

Authors: Kevin Dilks 1; T. Kyle Petersen 1; John R. Stembridge 1

  • 1 Department of Mathematics - University of Michigan

Let W be an irreducible affine Weyl group with Coxeter complex \Sigma, where W denotes the associated finite Weyl group and L the translation subgroup. The Steinberg torus is the Boolean cell complex obtained by taking the quotient of \Sigma by the lattice L. We show that the ordinary and flag h-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over W for a descent-like statistic first studied by Cellini. We also show that the ordinary h-polynomial has a nonnegative \gamma-vector, and hence, symmetric and unimodal coefficients. In the classical cases, we also provide expansions, identities, and generating functions for the h-polynomials of Steinberg tori.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Coxeter complex,\gamma-nonnegativity,descent statistic,Eulerian polynomial,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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