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.
Bibliographical noteFunding 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 .
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