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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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