Séminaire Lotharingien de Combinatoire, 80B.18 (2018), 12 pp.

Foster Tom and Stephanie van Willigenburg

Schur-positivity of Equitable Ribbons

Abstract. We study the Schur-positivity poset and its conjectured maximal connected elements, which are certain equitable ribbon Schur functions. In particular, we establish sufficient conditions for the difference of two ribbon Schur functions to be Schur-positive, and we deduce necessary conditions for the difference of two equitable ribbon Schur functions to be Schur-positive. We use this to confirm conjectures on maximal and minimal equitable ribbon Schur functions for many cases, including all chains.


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

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