Séminaire Lotharingien de Combinatoire, 80B.46 (2018), 12 pp.

Erik Aas, Darij Grinberg and Travis Scrimshaw

Multiline Queues with Spectral Parameters

Abstract. Using the description of multiline queues as functions on words, we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues. We show that the spectral weight of a word is invariant under a natural action of the symmetric group, giving a proof of the commutativity conjecture of Arita, Ayyer, Mallick, and Prolhac. We give a determinant formula for the spectral weight of a word, which gives a proof of a conjecture of the first author and Linusson.

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

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