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pro vyhledávání: '"Fulman, Jason"'
We obtain sharp bounds on the convergence rate of Markov chains on irreducible representations of finite general linear, unitary, and symplectic groups (in both odd and even characteristic) given by tensoring with Weil representations.
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Externí odkaz:
http://arxiv.org/abs/2407.12713
Autor:
Fulman, Jason
We use representation theory of the symmetric group S_n to prove Poisson limit theorems for the distribution of fixed points for three types of non-uniform permutations. First, we give results for the commutator of g and x where g and x are uniform i
Externí odkaz:
http://arxiv.org/abs/2406.12139
We prove that if G is a sufficiently large finite almost simple group of Lie type, then given a fixed nontrivial element x in G and a coset of G modulo its socle, the probability that x and a random element of the coset generate a subgroup containing
Externí odkaz:
http://arxiv.org/abs/2403.17291
Autor:
Fulman, Jason
In work on the two alleles Moran model, Ewens showed that the stationary distribution for the number of genes of one type can be approximated by a Beta distribution. In this short note, we provide a sharp error term for this approximation. We show th
Externí odkaz:
http://arxiv.org/abs/2307.13835
Autor:
Fulman, Jason
A paper by Boros, Little, Moll, Mosteig, and Stanley relates properties of a map defined on the space of rational functions to Eulerian polynomials. We link their work to the carries Markov chain, giving a new proof and slight generalization of one o
Externí odkaz:
http://arxiv.org/abs/2306.05529
Autor:
Fulman, Jason, Guralnick, Robert
Publikováno v:
Alg. Number Th. 18 (2024) 1189-1219
We study the conjugacy classes of the classical affine groups. We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups. We use these to get good upper bounds for the number of cl
Externí odkaz:
http://arxiv.org/abs/2112.15219
Autor:
Fulman, Jason, Guralnick, Robert
Motivated by questions in algebraic geometry, Yifeng Huang recently derived generating functions for counting mutually annihilating matrices and mutually annihilating nilpotent matrices over a finite field. We give a different derivation of his resul
Externí odkaz:
http://arxiv.org/abs/2111.09433
Autor:
Fulman, Jason, Petersen, T. Kyle
In this expository article, we highlight the direct connection between card shuffling and the functions known as $P$-partitions that come from algebraic combinatorics. While many (but not all) of the results we discuss are known, we give a unified tr
Externí odkaz:
http://arxiv.org/abs/2004.01659