English

Signed combinatorial interpretations in algebraic combinatorics

Combinatorics 2024-12-25 v3 Discrete Mathematics

Abstract

We prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmetric polynomials, as well as various bases in Schubert theory. The results are stated in the language of computational complexity, while the proofs are based on the effective M\"obius inversion.

Keywords

Cite

@article{arxiv.2406.13902,
  title  = {Signed combinatorial interpretations in algebraic combinatorics},
  author = {Igor Pak and Colleen Robichaux},
  journal= {arXiv preprint arXiv:2406.13902},
  year   = {2024}
}

Comments

23 pages, added Section 8 in v2, minor grammatical edits in v3, to appear in Algebraic Combinatorics