Results 61 to 70 of about 73,359 (215)
, 2008 Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of quasicrystals. We
A. Carpi +17 more
core +1 more source
The implications of generative artificial intelligence for mathematics education
School Science and Mathematics, EarlyView.Abstract Generative artificial intelligence has become prevalent in discussions of educational technology, particularly in the context of mathematics education. These AI models can engage in human‐like conversation and generate answers to complex questions in real‐time, with education reports accentuating their potential to make teachers' work more ...
Candace Walkington
wiley +1 more source
Random multilinear maps and the Erdős box problem
Discrete Analysis, 2021 Random multilinear maps and the Erdős box problem, Discrete Analysis 2021:17, 8 pp. A major theme in extremal combinatorics is determining the maximum number of edges that a graph or hypergraph can have if it does not contain a certain fixed graph or ...
David Conlon +2 more
doaj +1 more source
Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
wiley +1 more source
Forbidden intersection problems for families of linear maps
Discrete Analysis, 2023 Forbidden intersection problems for families of linear maps, Discrete Analysis 2023:19, 32 pp. A central problem in extremal combinatorics is to determine the maximal size of a set system given constraints on the sizes of the sets in the system and on ...
David Ellis, Guy Kindler, Noam Lifshitz
doaj +1 more source
Algebraic properties of word equations
, 2014 The question about maximal size of independent system of word equations is one of the most striking problems in combinatorics on words. Recently, Aleksi Saarela has introduced a new approach to the problem that is based on linear-algebraic properties of ...
Holub, Štěpán, Žemlička, Jan
core +1 more source
Thinning to Improve Two‐Sample Discrepancy
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT The discrepancy between two independent samples X1,…,Xn$$ {X}_1,\dots, {X}_n $$ and Y1,…,Yn$$ {Y}_1,\dots, {Y}_n $$ drawn from the same distribution on ℝd$$ {\mathbb{R}}^d $$ typically has order O(n)$$ O\left(\sqrt{n}\right) $$ even in one dimension.
Gleb Smirnov, Roman Vershynin
wiley +1 more source
On an Algorithm for Multiperiodic Words
Acta Polytechnica, 2013 We consider an algorithm by Tijdeman and Zamboni constructing a word of length k thathas periods p1, . . . , pr, and the richest possible alphabet.
Štepán Holub
doaj
Rhombic tilings and Bott-Samelson varieties
, 2016 S.~Elnitsky (1997) gave an elegant bijection between rhombic tilings of $2n$-gons and commutation classes of reduced words in the symmetric group on $n$ letters.
Escobar, Laura +3 more
core +1 more source
Dimer models and conformal structures
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala +3 more
wiley +1 more source