Related papers: Super-exponential 2-dimensional Dehn functions

Consider the operator $E$ on arithmetic functions such that $Ef$ is the multiplicative arithmetic function defined by $(Ef)(p^a) = f(a)$ for every prime power $p^a$. We investigate the behaviour of $E^m\tau_k$, where $\tau_k$ is a…

In recent, H. Sun defined a new kind of refined Eulerian polynomials, namely, \begin{eqnarray*} A_n(p,q)=\sum_{\pi\in \mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)} \end{eqnarray*} for $n\geq 1$, where ${odes}(\pi)$ and ${edes}(\pi)$…

Let $X\subset\mathbb{R}^n$ be a convex closed and semialgebraic set and let $f$ be a polynomial positive on $X$. We prove that there exists an exponent $N\geq 1$, such that for any $\xi\in\mathbb{R}^n$ the function…

We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…

We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…

The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous…

We consider exponential ultradistribution semigroups with non--densely defined generators and give structural theorems for ultradistribution semigroups. Also structural theorems for exponential ultradistribution semigroups are given.

For $q \in (0, 1)$, the deformed exponential function $f(x) = \sum_{n \geq 1} x^n q^{n(n-1)/2}/n!$ is known to have infinitely many simple and negative zeros $\{x_k(q)\}_{k \geq 1}$. In this paper, we analyze the series expansions of…

We prove that Abels' group over an arbitrary nondiscrete locally compact field has a quadratic Dehn function. As applications, we exhibit connected Lie groups and polycyclic groups whose asymptotic cones have uncountable abelian fundamental…

We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of mapping class groups by large powers of Dehn twists are…

The 4-dimensional model with topological mass generation that has recently been presented by Dvali, Jackiw and Pi [G. Dvali, R. Jackiw, and S.-Y. Pi, Phys. Rev. Lett. 96, 081602 (2006), hep-th/0610228] is generalized to any even number of…

We give examples of CAT(0), biautomatic, free-by-cyclic, one-relator groups which have finite-rank free subgroups of huge (Ackermannian) distortion. This leads to elementary examples of groups whose Dehn functions are similarly extravagant.…

We propose a relatively new notion of two-valued elements, which arises naturally in constructing the star exponential functions of the quad-ratics in the Weyl algebra over the complex number field. This notion enables us to describe the…

The filling volume functions of the n-th quaternionic Heisenberg group grow, up to dimension n, as fast as the ones of the Euclidean space. We identify the growth rate of the filling volume function in dimension n+1, which is strictly…

In differential geometry, the notation d^n f along with the corresponding formalism has fallen into disuse since the birth of exterior calculus. However, differentials of higher order are useful objects that can be interpreted in terms of…

We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of…

We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over…

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by…

We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie group there is a maximum equivalence class of length…

We show that the conjugator length function of the Baumslag-Gersten group is bounded above and below by a tower of exponentials of logarithmic height -- in particular it grows faster than any tower of exponentials of fixed height. We…