Computational complexity, Newton polytopes, and Schubert polynomials

An efficient algorithm for deciding vanishing of Schubert polynomial coefficients

“…By (12) and Proposition 2.3, we have (1) , D (2) D. Thus, by Claims 2.20 and 2.21 and induction, there exist τ D (1) ∈ PerfectTab(D (1) , α (1) ) and τ D (2) ∈ PerfectTab(D (2) , α (2) ).…”

“…Related discussion of complexity and the "nonvanishing problem" in algebraic combinatorics appears in the conference proceedings [1] and preprint [2] versions of this paper. ⋆ ( ( ( (…”

“…Clearly τ D is flagged and satisfies τ −1 D ({•}) = ∅. It has content α because α = α (1) + α (2) , and it is column-injective because the images of τ D (1) and τ D (2) are disjoint. Therefore, τ D ∈ PerfectTab(D, α) and Case 2b is complete.…”