Related papers: Poset vectors and generalized permutohedra
In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Gamma^{p,q} with p greater or equal to q. It is known that if the lattice is at most Lorentzian, the…
We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattices. We use a symmtery approach for Poisson structures that generalizes the Poisson…
Circuits and extended formulations are classical concepts in linear programming theory. The circuits of a polyhedron are the elementary difference vectors between feasible points and include all edge directions. We study the connection…
Let $G$ be an acylic directed graph. For each vertex $g \in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$. Trim lattices…
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a…
Given a finite Coxeter system $(W,S)$ and a Coxeter element $c$, we construct a simple polytope whose outer normal fan is N. Reading's Cambrian fan $F_c$, settling a conjecture of Reading that this is possible. We call this polytope the…
Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincar\'e-extended ab-index, which generalizes both the ab-index and the Poincar\'e polynomial.…
The standard method for constructing generating vectors for good lattice point sets is the component-by-component construction. Numerical experiments have shown that the generating vectors found by these constructions sometimes tend to have…
We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…
We generalize condensed motives, through Witt vectors and the associated moduli stacks of generalized line bundles.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
We prove that Bethe vectors generically form a base in a tensor product of irreducible heighest weight $gl_2$-modules or $U_q(gl_2)$-modules. We apply this result to difference equations with regular singular points. We show that if such an…
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole…
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…
For a left vector space V over a totally ordered division ring F, let Co(V) denote the lattice of convex subsets of V. We prove that every lattice L can be embedded into Co(V) for some left F-vector space V. Furthermore, if L is finite…
We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\hat{p}_q$, and its canonically…
This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and…
The linear extension diameter of a finite poset P is the maximum distance between a pair of linear extensions of P, where the distance between two linear extensions is the number of pairs of elements of P appearing in different orders in…