Related papers: String C-groups of 2-power order project onto a co…

We describe the automorphism groups of reductive monoids and of root monoids with active groups of invertible elements.

We show that the $\gamma$-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable spheres which includes all polytopes. The…

We compute partition functions describing multiplicities and charges of massless and first massive string states of pure-spinor superstrings in 3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet of minimal…

Let $T$ be a tree and $e$ an edge in $T$. If $C$ is a component of $T\setminus e$ and both $C$ and its complement are infinite we say that $C$ is a half-tree. The main result of this paper is that if $G$ is a closed subgroup of the…

We discuss a Clifford algebra framework for discrete symmetry groups (such as reflection, Coxeter, conformal and modular groups), leading to a surprising number of new results. Clifford algebras allow for a particularly simple description…

We study elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs from their modularity and explore the relation to topological string partition functions. We find a novel kinematical constraint that elliptic genera should follow, which…

Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their $f$--vectors and checking the validity of the following five conjectures: B\'{a}r\'{a}ny, unimodality, $3^d$, flag and cubical lower…

For any Kahler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points…

We show that the $f$-vector sets of $d$-polytopes have non-trivial additive structure: They span affine lattices and are embedded in monoids that we describe explicitly. Moreover, for many large subclasses, such as the simple polytopes, or…

Abstract polytopes are a combinatorial generalization of convex and skeletal polytopes. Counting how many flag orbits a polytope has under its automorphism group is a way of measuring how symmetric it is. Polytopes with one flag orbit are…

We give an exact characterization of monotone graph classes C with bounded average degree that satisfy the following property: The domination number of every graph from C is bounded by a linear function of its 2-independence number.

Say that a separable, unital C*-algebra D is strongly self-absorbing if there exists an isomorphism $\phi: D \to D \otimes D$ such that $\phi$ and $id_D \otimes 1_D$ are approximately unitarily equivalent $*$-homomorphisms. We study this…

This paper is devoted to the study of special subgroups of the automorphism groups of Kronrod-Reeb graphs of a Morse functions on $2$-torus $T^2$ which arise from the action of diffeomorphisms preserving a given Morse function on $T^2$. In…

The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…

A simplicial polytope is a polytope with all its facets being combinatorially equivalent to simplices. We deal with the edge connectivity of the graphs of simplicial polytopes. We first establish that, for any $d\ge 3$, for any $d\ge 3$,…

Let $\mathcal{C}$ be a plane curve defined over the algebraic closure $K$ of a prime finite field $\mathbb{F}_p$ by a separated polynomial, that is $\mathcal{C}: A(y)=B(x)$, where $A(y)$ is an additive polynomial of degree $p^n$ and the…

We show in this work that homology in degree d of a congruence group, in a very general framework, defines a weakly polynomial functor of degree at most 2d and we describe this functor modulo polynomial functors of smaller degree. Our main…

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. We say that a graph $G$ is $d$-distinguishing critical, if…

The degree set of a finite simple graph $G$ is the set of distinct degrees of vertices of $G$. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set $\mathscr D$ is $1+\max \mathscr D$.…

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…