2020/12/11 by Eli Bagno, Bagno, Eli, Riccardo Biagioli +5
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2012.06412
openalex publication_date 2020/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group Bn, \FC(Bn), is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of \FC(Bn) into a disjoint union of two-sided Barbash-Vogan combinatorial cells, a type B extension of Rubey's descent preserving involution on 321-avoiding permutations and a detailed study of the intersection of \FC(Bn) with Sn-cosets which yields a new decomposition of \FC(Bn) into disjoint subsets called fibers. We also compare two different type B Schur-positivity notions, arising from works of Chow and Poirier