Signed combinatorial interpretations in algebraic combinatorics

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 Möbius inversion.

arXiv comment23 pages, added Section 8 in v2, minor grammatical edits in v3, to appear in Algebraic Combinatorics