Séminaire Lotharingien de Combinatoire, 82B.9 (2019), 12 pp.

Hiroshi Naruse and Soichi Okada

Skew hook formula for d-complete posets via equivariant K-theory

Abstract. Peterson and Proctor obtained a product formula for the multivariate generating function of P-partitions on a d-complete poset P in terms of hooks in P. In this article, we give a skew generalization of Peterson-Proctor's hook formula, i.e., a subtraction-free formula for the generating function of (P \ F)-partitions for a d-complete poset P and its order filter F. Our proof uses the equivariant K-theory of Kac-Moody partial flag varieties, and this generalization provides an alternate proof of Peterson-Proctor's hook formula.


Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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