Séminaire Lotharingien de Combinatoire, 80B.90 (2018), 12 pp.

Per Alexandersson, Jim Haglund, and George Wang

From Generalized Permutahedra to Grothendieck Polynomials via Flow Polytopes

Abstract. We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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