相关论文: Hochschild polytopes

We define and construct mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these…

This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well…

It is known that the $k$-faces of the permutohedron $\Pi_n$ are labeled by (all possible) linearly ordered partitions of the set $[n]=\{1,...,n\}$ into $(n-k)$ non-empty parts. The incidence relation corresponds to the refinement: a face…

The Monotone Upper Bound Problem asks for the maximal number M(d,n) of vertices on a strictly-increasing edge-path on a simple d-polytope with n facets. More specifically, it asks whether the upper bound M(d,n)<=M_{ubt}(d,n) provided by…

We notice that one of the Diophantine equations, $knm=2kn+2km+2nm$, arising in the universality originated Diophantine classification of simple Lie algebras, has interesting interpretations for two different sets of signs of variables. In…

We introduce topological notions of polytopes and simplexes, the latter being expected to play in p-adically closed fields the role played by real simplexes in the classical results of triangulation of semi-algebraic sets over real closed…

A graph $G$ on $n$ vertices of diameter $D$ is called $H$-palindromic if $\alpha(G,k) = \alpha(G,D-k)$ for all $k=0, 1, \dots, \left \lfloor{\frac{D}{2}}\right \rfloor$, where $\alpha(G,k)$ is the number of unordered pairs of vertices at…

In this note, we construct a family of semisimple Hopf algebras $H_{n,m}$ of dimension $n^m m!$ over a field of characteristic zero containing a primitive $n$th root of unity, where $n, m \geq 2$ are integers. The well-known…

Combinatorial Hopf algebras of trees exemplify the connections between operads and bialgebras. Painted trees were introduced recently as examples of how graded Hopf operads can bequeath Hopf structures upon compositions of coalgebras. We…

On the set of complex number $\mathbb{C}$ it is possible to define $n$-valued group for any positive integer $n$. The $n$-multiplication defines a symmetric polynomial $p_n = p_n(x, y, z)$ with integer coefficients. By the theorem on…

The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f-, h- and gamma-vectors. These polytopes include permutohedra, associahedra, graph-associahedra, simple graphic zonotopes, nestohedra,…

The monotone path polytope of a polytope $P$ encapsulates the combinatorial behavior of the shadow vertex rule (a pivot rule used in linear programming) on $P$. Computing monotone path polytopes is the entry door to the larger subject of…

A construction of hexagon relations - algebraic realizations of four-dimensional Pachner moves - is proposed. It goes in terms of "permitted colorings" of 3-faces of pentachora (4-simplices), and its main feature is that the set of…

Given a tree $T$, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in $T$. These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics,…

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of K\"ahler differentials. Here we generalize it for simplicial, graded and anticommutative…

For a $d$-dimensional polytope with $v$ vertices, $d+1\le v\le2d$, we calculate precisely the minimum possible number of $m$-dimensional faces, when $m=1$ or $m\ge0.62d$. This confirms a conjecture of Gr\"unbaum, for these values of $m$.…

Every n-edge colored n-regular graph G naturally gives rise to a simple abstract n-polytope, the colorful polytope of G, whose 1-skeleton is isomorphic to G. The paper describes colorful polytope versions of the associahedron and…

Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we…