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- W3046939505 abstract "The nonvanishing problem asks if a coefficient of a polynomial is nonzero. Many families of polynomials in algebraic combinatorics admit combinatorial counting rules and simultaneously enjoy having saturated Newton polytopes (SNP). Thereby, in amenable cases, nonvanishing is in the complexity class $NPcap coNP$ of problems with good characterizations. This suggests a new algebraic combinatorics viewpoint on complexity theory. This report discusses the case of Schubert polynomials. These form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. We give a tableau criterion for nonvanishing, from which we deduce the first polynomial time algorithm. These results are obtained from new characterizations of the Schubitope, a generalization of the permutahedron defined for any subset of the n x n grid, together with a theorem of A. Fink, K. M'{e}sz'{a}ros, and A. St. Dizier, which proved a conjecture of C. Monical, N. Tokcan, and the third author." @default.
- W3046939505 created "2020-08-10" @default.
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- W3046939505 date "2018-10-24" @default.
- W3046939505 modified "2023-09-23" @default.
- W3046939505 title "Computational complexity, Newton polytopes, and Schubert polynomials" @default.
- W3046939505 hasPublicationYear "2018" @default.
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