This paper investigates ultrafilters in the context of connectivity systems, defined as pairs (X,
f) where X is a finite set and f is a symmetric submodular function. Ultrafilters, essential in …

We study arrangements of slightly skewed tropical hyperplanes, called blades by A.
Ocneanu, on the vertices of a hypersimplex $\Delta_ {k, n} $, and we investigate the …

A survey is given of recent results on fine zonotopal tilings by cubes (briefly, cubillages) of
cyclic zonotopes. The main interest of this theory is that it is interrelated with the theory of …

The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and
combinatorial structures. Its study involves interesting combinatorial objects, such as …

Given a configuration A of n points in R d− 1, we introduce the higher secondary polytopes
Image 1, which have the property that Image 2 agrees with the secondary polytope of …

We say that two sets S, T⊂{1, 2,⋯, n} are chord separated if there does not exist a cyclically
ordered quadruple a, b, c, d of integers satisfying a, c∈ S∖ T and b, d∈ T∖ S. This is a …

Let π: R^ n → R^ d π: R n→ R d be any linear projection, let A be the image of the standard
basis. Motivated by Postnikov's study of postitive Grassmannians via plabic graphs and …

We prove the conjecture that the higher Tamari orders of Dimakis and M\" uller-Hoissen
coincide with the first higher Stasheff--Tamari orders. To this end, we show that the higher …

This paper investigates ultrafilters in the context of connectivity systems, defined as pairs
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …

The purpose of this paper is to establish a correspondence between the higher Bruhat
orders of Yu. I. Manin and V. Schechtman, and the cup-$ i $ coproducts defining Steenrod …