A two-sided analogue of the Coxeter complex
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020)
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For any Coxeter system (W, S) of rank n, we introduce an abstract boolean complex (simplicial poset) of dimension 2n − 1 which contains the Coxeter complex as a relative subcomplex. Faces are indexed by triples (J,w,K), where J and K are subsets of the set S of simple generators, and w is a minimal length representative for the double parabolic coset WJ wWK . There is exactly one maximal face for each element of the group W . The complex is shellable and thin, which implies the complex is a sphere for the finite Coxeter groups. In this case, a natural refinement of the h-polynomial is given by the “two-sided” W -Eulerian polynomial, i.e., the generating function for the joint distribution of left and right descents in W .
@article{DMTCS_2020_special_379_a35,
author = {Petersen, T. Kyle},
title = {A two-sided analogue of the {Coxeter} complex},
journal = {Discrete mathematics & theoretical computer science},
year = {2020},
volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
doi = {10.46298/dmtcs.6353},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6353/}
}
TY - JOUR AU - Petersen, T. Kyle TI - A two-sided analogue of the Coxeter complex JO - Discrete mathematics & theoretical computer science PY - 2020 VL - DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) UR - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6353/ DO - 10.46298/dmtcs.6353 LA - en ID - DMTCS_2020_special_379_a35 ER -
%0 Journal Article %A Petersen, T. Kyle %T A two-sided analogue of the Coxeter complex %J Discrete mathematics & theoretical computer science %D 2020 %V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) %U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6353/ %R 10.46298/dmtcs.6353 %G en %F DMTCS_2020_special_379_a35
Petersen, T. Kyle. A two-sided analogue of the Coxeter complex. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi: 10.46298/dmtcs.6353
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