2010/09/23 by Luis Serrano, Luís Serrano, Christian Stump +2 · 2 citations
Mathematics · #05A05 (Secondary) #05E05 #05E45 (Primary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05E05 #msc:05E45
paper · pdf · doi:10.48550/arxiv.1009.4690
16 pages, 7 figures, revised version
openalex publication_date 2010/09/23 · arxiv created 2011/07/05 · arxiv updated 2011/07/07 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
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 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 of length 2(n-2k). Using this, we translate a conjectured cyclic sieving phenomenon for k-triangulations with rotation to the language of k-flagged tableaux with promotion.