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arXiv:2605.19063 · detector doi_compliance · incontrovertible · 2026-05-20 11:52:15.934464+00:00

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Geordie Williamson. Is deep learning a useful tool for the pure mathematician?CoRR, abs/2304.12602, 2023. doi: 10.48550/ARXIV .2304.12602. URL https://doi.org/10. 48550/arXiv.2304.12602. 13 Aq, t-Combinatorics Background & Narayana Models Triggered by the discovery of the famous Macdonald polynomials [19], q, t-combinatorics studies families of bivariate polynomials F(q, t) with nonnegative integer coefficients arising in a variety of mathematical domains. Historically, the first examples that attracted an intense research activity occurred in the study of the diagonal coinvariants of the symmetric group [ 16]. The bivariate polynomials arising from these algebraic objects keep track of the multiplicities of their “building blocks” (irreducible represen- tations): computing these multiplicities is the prototypical problem of representation theory. The q, t-Narayana polynomialsN n,k(q, t)are a notable example. Interest in q, t-combinatorics flourished over the past 25 years. Consequently, a formidable number of new formulas, conjectures, open problems, and interactions with other disciplines have been discovered. Among these new problems, a prominent role is played by the Type 1 and Type 2 problems mentioned in Section 4 [15, 9]. Our hope is that the methods presented in this paper will lead to breakthroughs in this fascinating area. The Type 2 problem of proving combinatorially the q, t-symmetry Nn,k(q, t) =N n,k(t, q) is one of the outstanding open problems of the theory. A 

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