Related papers: Orbit length generating functions of automorphisms…

Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$. In the present paper we consider profinite groups admitting a word $w$ such that the…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

Solvability of the rational quantum integrable systems related to exceptional root spaces $G_2, F_4$ is re-examined and for $E_{6,7,8}$ is established in the framework of a unified approach. It is shown the Hamiltonians take algebraic form…

The notion of a root functional of polynomials is a generalization of the notion of a root for a multiple root. A root functional is a linear functional that is defined on a polynomial ring and annuls the ideal of a system of polynomials. A…

Let $\mathbb{K}$ be an unramified quadratic extension of $\mathbb{Q}_{p}$ for a fixed $p>2$. Projective general linear groups $G=\operatorname{PGL}_{2}(\mathbb{K})$ and $H=\operatorname{PGL}_{2}(\mathbb{Q}_{p})$ act transitively on…

Working over an algebraically closed field of characteristic p > 3, we calculate the orbit closures in the Witt algebra W under the action of its automorphism group G. We also outline how the same techniques can be used to determine…

We introduce two operads which own the set of planar forests as a basis. With its usual product and two other products defined by different types of graftings, the algebra of planar rooted trees H becomes an algebra over these operads. The…

We characterize the bialgebraic varieties of the $\Gamma$ function, that is, if $V,W\subseteq\mathbb{C}^n$ are irreducible affine algebraic variety which satisfy $\dim V =\dim W$ and $\Gamma(V)\subseteq W$, then the equations defining $V$…

We establish a list of characterizations of bounded twin-width for hereditary, totally ordered binary structures. This has several consequences. First, it allows us to show that a (hereditary) class of matrices over a finite alphabet either…

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally…

Some of the consequences that follow from the C_2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C_2 condition has only finitely many n-point functions, and this result is used to…

The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with…

Let (X, g, J, f ) be a non-compact gradient shrinking Kahler-Ricci soliton. We prove that if the scalar curvature of X satisfies a mild assumption, then OP (X), the ring of holomorphic functions with polynomial growth on X, is finitely…

We classified finite orbits of monodromies of the Fuchsian system for five $2\times 2$ matrices. The explicit proof of this result is given. We have proposed a conjecture for a similar classification for $6$ or more $2\times 2$ matrices.…

Let G be a group of permutations of a denumerable set E. The profile of G is the function phi which counts, for each n, the number phi(n) of orbits of G acting on the n-subsets of E. Counting functions arising this way, and their associated…

Let $G$ and $\Omega$ be two planar domains. We give necessary and sufficient conditions on a sequence $(\phi_n)$ of eventually injective holomorphic mappings from $G$ to $\Omega$ for the existence of a function $f\in H(\Omega)$ whose orbit…

Given an operad P with a finite Groebner basis of relations, we study the generating functions for the dimensions of its graded components P(n). Under moderate assumptions on the relations we prove that the exponential generating function…

Abstract polytopes are combinatorial structures with distinctive geometric, algebraic, or topological characteristics, that generalize (the face lattice of) traditional polyhedra, polytopes or tessellations. Most research has focused on…

For a composition $f=f_1\circ\cdots \circ f_r$ of polynomials $f_i\in \mathbb Q[x]$ of degrees $d_i\geq 5$ with alternating or symmetric monodromy group, we show that the monodromy group of $f$ contains the iterated wreath product…

Given a function field $K$ and $\phi \in K[x]$, we study two finiteness questions related to iteration of $\phi$: whether all but finitely many terms of an orbit of $\phi$ must possess a primitive prime divisor, and whether the Galois…