Related papers: Smallest posets with given cyclic automorphism gro…

A graph $G$ of order $n$ is called edge-pancyclic if, for every integer $k$ with $3 \leq k \leq n$, every edge of $G$ lies in a cycle of length $k$. Determining the minimum size $f(n)$ of a simple edge-pancyclic graph with $n$ vertices…

A $3$-partition of an $n$-element set $V$ is a triple of pairwise disjoint nonempty subsets $X,Y,Z$ such that $V=X\cup Y\cup Z$. We determine the minimum size $\varphi_3(n)$ of a set $\mathcal{E}$ of triples such that for every 3-partition…

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x W_L^\theta$, where $x$ is an element of $W$ and $W_L^\theta$ the subgroup of fixed points of an automorphism $\theta$ of order at most two of…

The $n$-cube is the poset obtained by ordering all subsets of $\{1,\ldots,n\}$ by inclusion, and it can be partitioned into $\binom{n}{\lfloor n/2\rfloor}$ chains, which is the minimum possible number. Two such decompositions of the…

We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.

We prove that, for $n\geq 3$, the minimal dimension of a model of the classifying space of the full braid group $B_n$, and of the pure braid group $P_n$, with respect to the family of virtually cyclic groups is $n$.

We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base…

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a…

We observe that, for each positive integer n > 2, each of the Artin groups of finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is a central extension of a finite index subgroup of the mapping class group of the…

A configuration of points and lines is cyclic if it has an automorphism which permutes its points in a full cycle. A closed formula is derived for the number of non-isomorphic connected cyclic configurations of type (v_3), i.e., which have…

Let $\Gamma$ be a crystallographic group of dimension $n,$ i.e. a discrete, cocompact subgroup of $\operatorname{Isom}(\mathbb{R}^n)$ = $O(n)\ltimes\mathbb{R}^n.$ For any $n\geq 2,$ we construct a crystallographic group with a trivial…

A group in which every element commutes with its endomorphic images is called an $E$-group. If $p$ is a prime number, a $p$-group $G$ which is an $E$-group is called a $pE$-group. Every abelian group is obviously an $E$-group. We prove that…

We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…

We hope to see how much for a model M of some completion T of PA (Peano Arithmetic) does M restriction {<} determine M, say up to isomorphism. We advance in characterizing for non-standard models M of PA the "minimal" set {(a,b):n < a < b…

Let Cr(k) be the Cremona group of rank 2 over a field k, i.e. the group of all k-automorphisms of k(X,Y). We determine the l.c.m. of the orders of the finite subgroups of Cr(k) of order prime to the characteristic of k.

We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist…

A $k$-cycle in a graph is a cycle of length $k.$ A graph $G$ of order $n$ is called edge-pancyclic if for every integer $k$ with $3\le k\le n,$ every edge of $G$ lies in a $k$-cycle. It seems difficult to determine the minimum size $f(n)$…

In this article, we consider the problem of computing minimum dominating set for a given set $S$ of $n$ points in $\IR^2$. Here the objective is to find a minimum cardinality subset $S'$ of $S$ such that the union of the unit radius disks…

An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only…

We characterize the number of points for which there exist non-empty Terracini sets of points in $\mathbb{P}^n$. Then we study minimally Terracini finite sets of points in $\mathbb{P}^n$ and we obtain a complete description in the case of…