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I think I understand, though I haven't checked in great detail, nor attempted a naive proof. (So perhaps this doesn't count as an answer.) Given a Schubert polynomial, consider the terms containing $ …

I believe most of what you want is in https://arxiv.org/abs/math/0308101 , especially the polynomiality you're looking for. Note that that was first proven in [H. Derksen, J. Weyman] "On the Littlewoo …

Let S := the nonnegative integer solutions to {$a_1 + ... + a_n = n$}, and center := (1,1,1,...,1). Call a vector v generic if v.s = v.center <=> s = center. Then each generic v defines a positive sys …

In Hall's Marriage Theorem, we have a set $B$ of brides and $G$ of grooms, where each bride $b$ has an acceptable set $A_b \subseteq G$ of grooms. A matching $m:B\to G$ is an injection such that $m(b) …

No locking, even if you restrict to translations. Scale the whole arrangement up by a factor of $c$, then scale each polyhedron down by $c$ around its center of mass. Neither step introduces collision …

This is a weird case where I think the question actually asked is interesting, and that if I try to answer it I won't answer the question intended, which is less interesting. Here goes... The Schuber …

Naively, there can be no reasonable way of distinguishing the red nodes from green in the case $A_{even}$, as the Dynkin diagram automorphism switches them. Less naively, there is indeed a way of dis …

Matthias Lederer and I are studying a deformation of the Littlewood-Richardson product of Schur functions. It's a bit complicated to define (and work in progress) so I won't give the full definition h …

My M2 permutation code is here: http://www.math.cornell.edu/~allenk/permutation.m2 It's got a bunch of specialized stuff about Rothe diagrams and Fulton's essential set, but at the end it's got a Bruh …

Instead of thinking of the double Schubert polynomial $S_u$ as representing $[\overline{B_- uB}/B] \in H^*_T(GL_n/B)$, equivalently think of it as representing $[\overline{B_- uB}] \in H^*_{T\times B} …

Let $A$ be the directed adjacency matrix of an acyclic directed graph, with variables as its nonzero entries (one for each edge). The $(a,b)$ entry of the matrix $(I-A)^{-1}$ is the sum over all paths …

I apologize for asking questions that seem likely to be answered in Conway & Sloane's "Sphere Packings, Lattices, and Groups" if I knew where to look. Let $L$ be the unique* even unimodular lattice o …

One thing that is commonly done is to fix an initial polytope $P$, and consider all the polytopes whose fans are coarsenings of $P$'s fan. You can parametrize these by the space of convex piecewise-li …

I think it's because we have well-developed techniques with which to prove that this condition holds, and when those fail, people don't put that much effort into trying to describe the (more difficult …

Let $m$ be any $W$-invariant compactly supported $\mathbb Z$-valued function on the weight lattice. Then to expand $m$ in the basis of weight multiplicity functions of irreps, first apply differencing …