Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Sean Eberhard"'
Publikováno v:
Discrete Analysis (2016)
Permutations contained in transitive subgroups, Discrete Analysis 2016:12, 36 pp. This paper is part of a series. The previous paper in the series [2] concerned the following question. A property of elements $x_1,\dots,x_t$ of a group $G$ is said to
Externí odkaz:
https://doaj.org/article/fcc4b8086f194eaa82d6fd383d2479bf
Autor:
Sean Eberhard
Publikováno v:
Discrete Analysis (2016)
Product mixing in the alternating group, Discrete Analysis 2016:2, 18 pp. Growth and mixing of subsets of groups is a major theme in group theory. The former concerns lower bounds for the sizes of product sets, especially of the form $A^k$, where $A
Externí odkaz:
https://doaj.org/article/5cfd1bd571fd45be9b9420b1d49c4b61
Autor:
Sean Eberhard, Pavel Shumyatsky
Publikováno v:
Eberhard, S & Shumyatsky, P 2023, ' Probabilistically nilpotent groups of class two ', Mathematische Annalen . https://doi.org/10.1007/s00208-023-02567-0
For $G$ a finite group, let $d_2(G)$ denote the proportion of triples $(x, y, z) \in G^3$ such that $[x, y, z] = 1$. We determine the structure of finite groups $G$ such that $d_2(G)$ is bounded away from zero: if $d_2(G) \geq \epsilon > 0$, $G$ has
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::24de07dadf77c2474b6f99b7d5541753
https://pure.qub.ac.uk/en/publications/329ea372-3fdc-4442-9766-fb919c959db7
https://pure.qub.ac.uk/en/publications/329ea372-3fdc-4442-9766-fb919c959db7
Publikováno v:
Combinatorics, Probability and Computing. 30:899-904
A family of vectors $A \subset [k]^n$ is said to be intersecting if any two elements of $A$ agree on at least one coordinate. We prove, for fixed $k \ge 3$, that the size of a symmetric intersecting subfamily of $[k]^n$ is $o(k^n)$, which is in stark
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d4fde64e38e810a092e99b644129ac4
https://doi.org/10.1017/s0963548321000079
https://doi.org/10.1017/s0963548321000079
Autor:
Daniele Garzoni, Sean Eberhard
Publikováno v:
Algebraic Combinatorics. 4:1-25
We study random generation in the symmetric group when cycle type restrictions are imposed. Given $\pi, \pi' \in S_n$, we prove that $\pi$ and a random conjugate of $\pi'$ are likely to generate at least $A_n$ provided only that $\pi$ and $\pi'$ have
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::437291480eccbf4e2f0f6114e7d76ae3
https://doi.org/10.5802/alco.149
https://doi.org/10.5802/alco.149
Publikováno v:
Combinatorics, Probability and Computing. 30:800-810
Let $P(n)$ be the probability that two independent, uniformly random permutations of $[n]$ have the same order, and let $K(n)$ be the probability that they are in the same conjugacy class. Answering a question of Thibault Godin, we prove that $ P(n)=
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b00273852bede4f02e84deef6fc75d8
https://doi.org/10.1017/s0963548321000043
https://doi.org/10.1017/s0963548321000043
Autor:
Sean Eberhard
Publikováno v:
Advances in Geometry
Here is a simplified proof that every sharply transitive subset of PGL2(K) is a coset of a subgroup, for every finite field K.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ca6cceefbf1f90de51f7982b2f7832b7
https://doi.org/10.1515/advgeom-2021-0029
https://doi.org/10.1515/advgeom-2021-0029
Autor:
Sean Eberhard, Urban Jezernik
Let $G = \mathrm{SCl}_n(q)$ be a quasisimple classical group with $n$ large, and let $x_1, \dots, x_k \in G$ random, where $k \geq q^C$. We show that the diameter of the resulting Cayley graph is bounded by $q^2 n^{O(1)}$ with probability $1 - o(1)$.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dea3f1c4666f70a27ca7e21bd8f4d1fa
http://arxiv.org/abs/2005.09990
http://arxiv.org/abs/2005.09990
Autor:
Sean Eberhard
Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $\phi$ be the characteristic polynomial. Conditionally on the extended Riemann hypothes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a16300872ae72c107cc3f39c8c099ba
Autor:
Péter P. Varjú, Sean Eberhard
Publikováno v:
Probability Theory and Related Fields
Define $(X_n)$ on $\mathbf{Z}/q\mathbf{Z}$ by $X_{n+1} = 2X_n + b_n$, where the steps $b_n$ are chosen independently at random from $-1, 0, +1$. The mixing time of this random walk is known to be at most $1.02 \log_2 q$ for almost all odd $q$ (Chung-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f27cce964afa7975cceb677b26bfc37a