Related papers: Generators of the plane Cremona group over the fie…

We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.

A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a…

In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane.

We use the concept of production matrices to show that there exist sets of $n$ points in the plane that admit $\Omega(42.11^n)$ crossing-free geometric graphs. This improves the previously best known bound of $\Omega(41.18^n)$ by Aichholzer…

A subset $\left\{x_{1},x_{2},\hdots,x_{d}\right\}$ of a group $G$ \emph{invariably generates} $G$ if $\left\{x_{1}^{g_{1}},x_{2}^{g_{2}},\hdots,x_{d}^{g_{d}}\right\}$ generates $G$ for every $d$-tuple $(g_{1},g_{2}\hdots,g_{d})\in G^{d}$.…

Let G(q) be the group of permutations of the finite field F_q which is generated by those permutations that can be written as c-->ac^m+bc^n with 0<m<n<q and a,b in F_q with ab nonzero. We show that there are infinitely many q for which G(q)…

Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultaneous conjugation by $GL_n$ is generated by traces of products of generic matrices. In this paper we have found, in terms of…

We prove that both the hyperelliptic mapping class group and the extended hyperelliptic mapping class group are generated by two torsion elements. We also compute the index of the subgroup of the hyperelliptic mapping class group which is…

Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this…

We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient…

Let $S(n)$, for $n \in \mathbb{N}$, be the infinite-type surface of infinite genus with $n$ ends, each accumulated by genus. Although the mapping class groups of these surfaces are not countably generated,they are Polish groups and hence…

We consider the infinite family of Feynman graphs known as the "banana graphs" and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern-Schwartz-MacPherson…

We generate all the finite kneading sequences of one of the two kinds of bimodal map on the interval, building each sequence uniquely from a pair of shorter ones. There is a single pair at generation 0, with members of length 1. Concomitant…

We construct $(2,3)$-generators for the finite $8$-dimensional orthogonal groups, proving the following results: the groups $\Omega_8^+(q)$ and $P\Omega_8^+(q)$ are $(2,3)$-generated if and only if $q\geq 4$; the groups $\Omega_8^-(q)$ and…

The mapping class group of an orientable surface, which records its symmetries up to isotopy, plays a central role in low-dimensional topology. This chapter explores the foundational problem of determining minimal generating sets for these…

We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which…

Let Mod_{g,b} denote the mapping class group of a surface of genus g with b punctures. Feng Luo asked in a recent preprint if there is a universal upper bound, independent of genus, for the number of torsion elements needed to generate…

We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

We prove that for genus $g=3,4$, the extended mapping class group $\text{Mod}^{\pm}(S_g)$ can be generated by two elements of finite orders. But for $g=1$, $\text{Mod}^{\pm}(S_1)$ cannot be generated by two elements of finite orders.