English

A combinatorial skewing formula for the Rise Delta Theorem

Combinatorics 2024-08-23 v1

Abstract

We prove that the symmetric function Δek1en\Delta'_{e_{k-1}}e_n appearing in the Delta Conjecture can be obtained from the symmetric function in the Rational Shuffle Theorem by applying a Schur skewing operator. This generalizes a formula by the first and third authors for the Delta Conjecture at t=0t=0, and follows from work of Blasiak, Haiman, Morse, Pun, and Seelinger. Our main result is that we also provide a purely combinatorial proof of this skewing identity, giving a new proof of the Rise Delta Theorem from the Rational Shuffle Theorem.

Keywords

Cite

@article{arxiv.2408.12543,
  title  = {A combinatorial skewing formula for the Rise Delta Theorem},
  author = {Maria Gillespie and Eugene Gorsky and Sean T. Griffin},
  journal= {arXiv preprint arXiv:2408.12543},
  year   = {2024}
}
R2 v1 2026-06-28T18:21:04.233Z