English

On the Bivariate Characteristic Polynomial of the Shuffle Lattice

Combinatorics 2024-09-26 v1

Abstract

The shuffle lattice was introduced by Greene in 1988 as an idealized model for DNA mutation, when he revealed remarkable combinatorial properties of this structure. In this paper, we prove an explicit formula for the MM-triangle of the shuffle lattice, a bivariate refinement of the characteristic polynomial, as conjectured by McConville and M\"uhle in 2022, and find a relation between the MM-triangle and the HH-triangle, a bivariate refinement of the rank generating function.

Keywords

Cite

@article{arxiv.2409.17123,
  title  = {On the Bivariate Characteristic Polynomial of the Shuffle Lattice},
  author = {Annabel Ma},
  journal= {arXiv preprint arXiv:2409.17123},
  year   = {2024}
}

Comments

21 pages, 3 figures