Results 11 to 20 of about 280 (40)

The system of sets of lengths in Krull monoids under set addition [PDF]

, 2015
Let $H$ be a Krull monoid with class group $G$ and suppose that each class contains a prime divisor. Then every element $a \in H$ has a factorization into irreducible elements, and the set $\mathsf L (a)$ of all possible factorization lengths is the set ...
Geroldinger, Alfred, Schmid, Wolfgang
core   +4 more sources

A DISTRIBUTION ON TRIPLES WITH MAXIMUM ENTROPY MARGINAL

Forum of Mathematics, Sigma, 2019
We construct an $S_{3}$-symmetric probability distribution on $\{(a,b,c)\in \mathbb{Z}_{{\geqslant}0}^{3}\,:\,a+b+c=n\}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots ,n\}$ with mean $n/3 ...
SERGEY NORIN
doaj   +1 more source

ROTH’S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS

Forum of Mathematics, Sigma, 2016
We show that if $A\subset \{1,\ldots ,N\}$ does not contain any nontrivial solutions to the equation
TOMASZ SCHOEN, OLOF SISASK
doaj   +1 more source

UPPER BOUNDS FOR SUNFLOWER-FREE SETS

Forum of Mathematics, Sigma, 2017
A collection of $k$ sets is said to form a $k$ -sunflower ...
ERIC NASLUND, WILL SAWIN
doaj   +1 more source

Small doubling in groups [PDF]

, 2013
Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A|
A. G. Vosper, A. L. Cauchy, A. Lubotzky, A. Lubotzky, A. S. Golsefidy, B. Green, B. Green, B. Green, B. Green, B. Green, C. Even-Zohar, D. Fisher, E. Breuillard, E. Breuillard, E. Breuillard, E. Croot, E. Hrushovski, G. A. Freiman, G. A. Freiman, G. A. Margulis, G. Elekes, G. Petridis, H. A. Helfgott, H. A. Helfgott, H. Davenport, I. Z. Ruzsa, I. Z. Ruzsa, I. Z. Ruzsa, J. Bourgain, J. Bourgain, J. D. Dixon, L. Dries van den, M. Gromov, M. J. Larsen, M. Kassabov, M. Kneser, M.-C. Chang, M.-C. Chang, P. P. Varjú, P. Sarnak, P. Sarnak, R. I. Grigorchuk, R. J. Gardner, S. Hoory, S. R. Safin, S. V. Konyagin, T. Coulhon, T. Sanders, T. Sanders, T. Sanders, T. Sanders, T. Schoen, T. Tao, T. Tao, T. Tao, V. F. Lev, W. T. Gowers, W. T. Gowers, W. Woess, Y. Shalom, Y. Stanchescu, Y. Stanchescu   +61 more
core   +1 more source

Polynomial progressions in topological fields

Forum of Mathematics, Sigma
Let $P_1, \ldots , P_m \in \mathbb {K}[\mathrm {y}]$ be polynomials with distinct degrees, no constant terms and coefficients in a general local field $\mathbb {K}$ . We give a quantitative count of the number of polynomial progressions $
Ben Krause, Mariusz Mirek, Sarah Peluse, James Wright   +3 more
doaj   +1 more source

Visible Points On Exponential Curves

, 2017
We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible points on exponential curves modulo a prime for almost all primes.Comment: 8 ...
Macourt, Simon
core   +1 more source

Local aspects of the Sidorenko property for linear equations

Forum of Mathematics, Sigma
A system of linear equations in $\mathbb {F}_p^n$ is Sidorenko if any subset of $\mathbb {F}_p^n$ contains at least as many solutions to the system as a random set of the same density, asymptotically as $n\to \infty $ .
Daniel Altman
doaj   +1 more source

A Correspondence Principle for the Gowers Norms

, 2012
We give a variation of the Furstenberg Correspondence which preserves the Gowers uniformity norms.Comment: Journal of Logic and Analysis, 4; February ...
Towsner, Henry
core   +2 more sources

Relative rank and regularization

Forum of Mathematics, Sigma
We introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength).
Amichai Lampert, Tamar Ziegler
doaj   +1 more source