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The set of forks is a class of quivers introduced by M. Warkentin, where every connected mutation-infinite quiver is mutation equivalent to infinitely many forks. Let $Q$ be a fork with $n$ vertices, and $\boldsymbol{w}$ be a fork-preserving mutation
Externí odkaz:
http://arxiv.org/abs/2410.08510
Autor:
Ervin, Tucker J., Jackson, Blake
To better understand mutation-invariant and hereditary properties of quivers (and more generally skew-symmetrizable matrices), we have constructed a topology on the set of all mutation classes of quivers which we call the mutation class topology. Thi
Externí odkaz:
http://arxiv.org/abs/2403.20245
Autor:
Ervin, Tucker J.
The unrestricted red size of a quiver is the maximal number of red vertices in its framed quiver after any given mutation sequence. In a 2023 paper by E. Bucher and J. Machacek, it was shown that connected, mutation-finite quivers either have an unre
Externí odkaz:
http://arxiv.org/abs/2401.14958
Autor:
Ervin, Tucker J.
Publikováno v:
The Electronic Journal of Combinatorics Volume 31, Issue 1 (2024), Article P1.16
A hereditary property of quivers is a property preserved by restriction to any full subquiver. Similarly, a mutation-invariant property of quivers is a property preserved by mutation. Using forks, a class of quivers developed by M. Warkentin, we intr
Externí odkaz:
http://arxiv.org/abs/2306.07502
Autor:
Ervin, Tucker J., Jackson, Blake
In a post on the Open Problems in Algebraic Combinatorics (OPAC) blog, E. Bucher and J. Machacek posed three open problems: OPAC-033, OPAC-034, and OPAC-035. These three problems deal with the relationships between three infinite classes of quivers:
Externí odkaz:
http://arxiv.org/abs/2305.17194
Autor:
Ervin, Tucker J., Jackson, Blake, Lane, Jay, Lee, Kyungyong, Nguyen, Son Dang, O'Donohue, Jack, Vaughan, Michael
Publikováno v:
S\'eminaire Lotharingien de Combinatoire, B86a (2022), 15 pp
The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted $P$ (insertion) and $Q$ (recording). It has been an open problem to demonstrate $$ |\{w \in
Externí odkaz:
http://arxiv.org/abs/2108.08657
In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix representation of these reflections is determined by a linear ordering on th
Externí odkaz:
http://arxiv.org/abs/2108.03309
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