Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete
flag variety. We give a formula for the Castelnuovo–Mumford regularity of matrix Schubert …

The geometric naturality of Schubert polynomials and their combinatorial pipe dream
representations was established by Knutson and Miller (2005) via antidiagonal Gröbner …

We compute the expansion of the cohomology class of the permutahedral variety in the
basis of Schubert classes. The resulting structure constants are expressed as a sum of …

We construct an operator on sl. N/link homology with coefficients in a ring whose
characteristic divides N. If P is a prime number, we use this operator to exhibit structural …

The" back-stabilization number" for products of Schubert polynomials is the distance the
corresponding permutations must be shifted before the structure constants stabilize. We give …

This paper deals with decreasing operators on back stable Schubert polynomials. We study
two operators $\xi $ and $\nabla $ of degree $-1$, which satisfy the Leibniz rule …

We construct a simple combinatorially-defined representation of $\mathfrak {sl} _2 $ which
respects the order structure of the weak order on the symmetric group. This is used to prove …

We introduce two new partial orders on the standard Young tableaux of a given partition
shape, in analogy with the strong and weak Bruhat orders on permutations. Both posets are …

In recent work, the authors used an order lowering operator∇, introduced by Stanley, to
prove the strong Sperner property for the weak Bruhat order on the symmetric group …

We prove a formula for the image of a skew Schur polynomial $ s_ {\lambda/\mu}\left (x_ {1},
x_ {2},\ldots, x_ {N}\right) $ under the differential operator $\nabla:=\dfrac {\partial}{\partial x …