Séminaire Lotharingien de Combinatoire, 86B.48 (2022), 12 pp.

Pooneh Afsharijoo, Jehanne Dousse, Frédéric Jouhet and Hussein Mourtada

New Companions to Gordon Identities from Commutative Algebra

Abstract. We survey the ideas of a proof of a recent conjecture on partitions due to the first author, which was discovered in the study of arc spaces and differential algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve graded quotient rings, new Durfee-type dissections for integer partitions, and q-series identities.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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