Pavel Galashin

Plabic graphs and zonotopal tilings: PLABIC GRAPHS AND ZONOTOPAL TILINGS

We say that two sets

A Littlewood–Richardson rule for dual stable Grothendieck polynomials

S,T\subset\{1,2,\dots,n\}

Manifolds associated to simple games

are chord separated if there does not exist a cyclically ordered quadruple

Weak separation, pure domains and cluster distance

a,b,c,d

Extensions of isometric embeddings of pseudo-Euclidean metric polyhedra

of integers satisfying

Existence of a persistent hub in the convex preferential attachment model

a,c\in S-T

Parity duality for the amplituhedron

and

The classification of Zamolodchikov periodic quivers

b,d\in T-S

Purity and separation for oriented matroids

. This is a weaker version of Leclerc and Zelevinskys weak separation. We show that every maximal by inclusion collection of pairwise chord separated sets is also maximal by size. Moreover, we prove that such collections are precisely vertex label collections of fine zonotopal tilings of the three-dimensional cyclic zonotope. In our construction, plabic graphs and square moves appear naturally as horizontal sections of zonotopal tilings and their mutations respectively.

Root system chip-firing I: interval-firing

Abstract For a given skew shape, we build a crystal graph on the set of all reverse plane partitions that have this shape. As a consequence, we get a simple extension of the Littlewood–Richardson rule for the expansion of the corresponding dual stable Grothendieck polynomial in terms of Schur polynomials.