Luis Serrano ; Christian Stump
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Generalized triangulations, pipe dreams, and simplicial spheres
dmtcs:2961 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
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https://doi.org/10.46298/dmtcs.2961
Generalized triangulations, pipe dreams, and simplicial spheresArticle
Authors: Luis Serrano 1; Christian Stump 1
0000-0002-5276-1392##NULL
Luis Serrano;Christian Stump
1 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
We exhibit a canonical connection between maximal $(0,1)$-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable and thus a shellable sphere. In particular, this implies a positivity result for Schubert polynomials. For Ferrers shapes, we moreover construct a bijection to maximal fillings avoiding south-east chains of the same length which specializes to a bijection between $k$-triangulations of the $n$-gon and $k$-fans of Dyck paths. Using this, we translate a conjectured cyclic sieving phenomenon for $k$-triangulations with rotation to $k$-flagged tableaux with promotion.
Sara Billey;Alexander Holroyd;Benjamin Young, 2020, A bijective proof of Macdonald's reduced word formula, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings, 28th..., 10.46298/dmtcs.6412, https://doi.org/10.46298/dmtcs.6412.
ANATOL N. KIRILLOV, 2012, ON SOME ALGEBRAIC AND COMBINATORIAL PROPERTIES OF DUNKL ELEMENTS, International Journal of Modern Physics B, 26, 27n28, pp. 1243012, 10.1142/s0217979212430126.