Zobrazeno 1 - 10
of 180
pro vyhledávání: '"WILDON, MARK"'
Let $G$ be a finite group and let $H$ be a subgroup of $G$. The left-invariant random walk driven by a probability measure $w$ on $G$ is the Markov chain in which from any state $x \in G$, the probability of stepping to $xg \in G$ is $w(g)$. The init
Externí odkaz:
http://arxiv.org/abs/2412.19742
Autor:
Glazer, Elliot, Erdil, Ege, Besiroglu, Tamay, Chicharro, Diego, Chen, Evan, Gunning, Alex, Olsson, Caroline Falkman, Denain, Jean-Stanislas, Ho, Anson, Santos, Emily de Oliveira, Järviniemi, Olli, Barnett, Matthew, Sandler, Robert, Vrzala, Matej, Sevilla, Jaime, Ren, Qiuyu, Pratt, Elizabeth, Levine, Lionel, Barkley, Grant, Stewart, Natalie, Grechuk, Bogdan, Grechuk, Tetiana, Enugandla, Shreepranav Varma, Wildon, Mark
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from computationally intensiv
Externí odkaz:
http://arxiv.org/abs/2411.04872
Autor:
Martinez, Alvaro L., Wildon, Mark
Let $\mathbb{F}$ be a field and let $E$ be the natural representation of $\mathrm{SL}_2(\mathbb{F})$. Given a vector space $V$, let $\Delta^{(2,1^{N-1})}V$ be the kernel of the multiplication map $\bigwedge^N V \otimes V \rightarrow \bigwedge^{N+1}V$
Externí odkaz:
http://arxiv.org/abs/2405.04631
Autor:
Britnell, John R., Wildon, Mark
Let $Q$ be a probability measure on a finite group $G$, and let $H$ be a subgroup of $G$. We show that a necessary and sufficient condition for the random walk driven by $Q$ on $G$ to induce a Markov chain on the double coset space $H\backslash G/H$,
Externí odkaz:
http://arxiv.org/abs/2311.02723
The plethysm coefficient $p(\nu, \mu, \lambda)$ is the multiplicity of the Schur function $s_\lambda$ in the plethysm product $s_\nu \circ s_\mu$. In this paper we use Schur--Weyl duality between wreath products of symmetric groups and the ramified p
Externí odkaz:
http://arxiv.org/abs/2311.02721
Autor:
McDowell, Eoghan, Wildon, Mark
Let $E$ be the natural representation of the special linear group $\mathrm{SL}_2(K)$ over an arbitrary field $K$. We use the two dual constructions of the symmetric power when $K$ has prime characteristic to construct an explicit isomorphism $\mathrm
Externí odkaz:
http://arxiv.org/abs/2105.00538
Autor:
Britnell, John R., Wildon, Mark
This paper studies a family of random walks defined on the finite ordinals using their order reversing involutions. Starting at $x \in \{0,1,\ldots,n-1\}$, an element $y \le x$ is chosen according to a prescribed probability distribution, and the wal
Externí odkaz:
http://arxiv.org/abs/2102.08469
Autor:
Paget, Rowena, Wildon, Mark
Let $\nabla^\lambda$ denote the Schur functor labelled by the partition $\lambda$ and let $E$ be the natural representation of $\mathrm{SL}_2(\mathbb{C})$. We make a systematic study of when there is an isomorphism $\nabla^\lambda \!\mathrm{Sym}^\ell
Externí odkaz:
http://arxiv.org/abs/1907.07616
Autor:
Wildon, Mark
We use a coin flipping model for the random partition and Chebyshev's inequality to prove the lower bound $\lim \frac{\log p(n)}{\sqrt{n}} \ge C$ for the number of partitions $p(n)$ of $n$, where $C$ is an explicit constant.
Comment: 4 pages, 1
Comment: 4 pages, 1
Externí odkaz:
http://arxiv.org/abs/1905.10590
Autor:
Wildon, Mark
We use the hook lengths of a partition to define two rectangular tableaux. We prove these tableaux have equal multisets of entries, first by elementary combinatorial arguments, and then using Stanley's Hook Content Formula and symmetric polynomials.<
Externí odkaz:
http://arxiv.org/abs/1904.08904