Block number, descents and Schur positivity of fully commutative elements in Bn

Eli Bagno, Riccardo Biagioli, Frédéric Jouhet, Yuval Roichman

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number103464
JournalEuropean Journal of Combinatorics
StatePublished - Mar 2022

Bibliographical note

Funding Information:
E.B, R.B and F.J were partially supported by the Israeli Ministry of Science and Technology , and the French National Scientific Research Center (CNRS) , grant PRC 1656 , Y.R. was partially supported by the Israel Science Foundation , Grant No. 1970/18 .

Publisher Copyright:
© 2021 Elsevier Ltd


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