Related papers: The mean Dehn function of abelian groups

Let $d_k(n)$ denote the $k$-fold divisor function. For a wide range of large $q$ the expected bound $$\sum_{n\leq x\atop {n\equiv a(q)}}d_k(n)-\text { main term }\approx \sqrt {x/q}$$ is shown to be true in an average sense -- for all $k$.…

We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.

This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…

Refining a result of Erdos and Mays, we give asymptotic series expansions for the functions $A(x)-C(x)$, the count of $n\leq x$ for which every group of order $n$ is abelian (but not all cyclic), and $N(x)-A(x)$, the count of $n\leq x$ for…

The purpose of this paper is to present the extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the…

Given a compact Riemannian manifold (M n , g) with boundary $\partial$M , we give an estimate for the quotient $\partial$M f d$\mu$ g M f d$\mu$ g , where f is a smooth positive function defined on M that satisfies some inequality involving…

We study the growth of torsion in the abelianizations of finite index subgroups in finitely generated metabelian groups. This complements earlier work of Kar, Kropholler and the author which covered the finitely presented amenable groups.

D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary…

In this announcement we generalize the Markov-Kakutani fixed point theorem for abelian semi-groups of affine transformations extending it on some class of non-commutative semi-groups. As an interesting example we apply it obtaining a…

Let G_1 and G_2 be two groups. If a group homomorphism \varphi : G_1 \longrightarrow G_2 maps a \in G_1 into b \in G_2 such that \varphi(a) = b, then we say a degenerates to b and if every element of G_1 degenerates to elements in G_2, then…

If $G$ is a finite Abelian group, define $s_{k}(G)$ to be the minimal $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. Recently Bitz et al. proved that if $n = exp(G)$, then…

The maximal normal subgroup growth type of a finitely generated group is $n^{\log n}$. Very little is known about groups with this type of growth. In particular, the following is a long standing problem: Let $\Gamma$ be a group and $\Delta$…

In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…

We consider space functions $s(n)$ of finitely presented groups $G =< A\mid R> .$ (These functions have a natural geometric analog.) To define $s(n)$ we start with a word $w$ over $A$ of length at most $n$ equal to 1 in $G$ and use…

We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for…

In this paper, we are interested in a Neumann-type series for modified Bessel functions of the first kind which arises in the study of Dunkl operators associated with dihedral groups and as an instance of the Laguerre semigroup constructed…

We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer $R$ (i.e. finite abelian groups generated by at most $R$ elements), by proving an inverse theorem for 1-bounded functions of non-trivial…

In 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function $f$, they produce a finitely presented residually finite…

We consider Mertens' function M(x,q,a) in arithmetic progression, Assuming the generalized Riemann hypothesis (GRH), we show an upper bound that is uniform for all moduli which are not too large. For the proof, a former method of K.…

A function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left and right…