Zero-one Schubert polynomials
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We prove that if σ∈Sm is a pattern of w∈Sn, then we can express the Schubert polynomial 𝔖w as a monomial times 𝔖σ (in reindexed variables) plus a polynomial with nonnegative coefficients. This implies that the set of permutations whose Schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment. Using Magyar's orthodontia, we characterize this class by a list of twelve avoided patterns. We also give other equivalent conditions on 𝔖w being zero-one. In this case, the Schubert polynomial 𝔖w is equal to the integer point transform of a generalized permutahedron.
AuthorsFink, A; Mészáros, K; St. Dizier, A
- Mathematics 
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