Zero-one Schubert polynomials

We prove that if $$\sigma \in S_m$$σ ∈ S m is a pattern of $$w \in S_n$$w ∈ S n , then we can express the Schubert polynomial $$\mathfrak {S}_w$$S w as a monomial times $$\mathfrak {S}_\sigma $$S σ (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 $$\mathfrak {S}_w$$S w being zero-one. In this case, the Schubert polynomial $$\mathfrak {S}_w$$S w is equal to the integer point transform of a generalized permutahedron.