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pro vyhledávání: '"Mcdonough, Alex"'
Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion of consistency to describe classes of actions that respect deletion-con
Externí odkaz:
http://arxiv.org/abs/2407.03999
Autor:
Doolittle, Joseph, McDonough, Alex
Publikováno v:
Discrete & Computational Geometry, 2024
It is broadly known that any parallelepiped tiles space by translating copies of itself along its edges. In earlier work relating to higher-dimensional sandpile groups, the second author discovered a novel construction which fragments the parallelpip
Externí odkaz:
http://arxiv.org/abs/2307.07900
Much of dynamical algebraic combinatorics focuses on global dynamical systems defined via maps that are compositions of local toggle operators. The second author and Roby studied such maps that result from toggling independent sets of a path graph. W
Externí odkaz:
http://arxiv.org/abs/2305.07627
Autor:
Black, Alexander E., Liu, Kevin, Mcdonough, Alex, Nelson, Garrett, Wigal, Michael C., Yin, Mei, Yoo, Youngho
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that the problem of generating planar tanglegrams uniformly at random reduces
Externí odkaz:
http://arxiv.org/abs/2304.05318
Autor:
Araujo, Igor, Black, Alexander E., Burcroff, Amanda, Gao, Yibo, Krueger, Robert A., McDonough, Alex
Given two vectors $u$ and $v$, their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$. If the entries of $u$ and $v$ are increasing and sufficiently generic, the total ordering of the entries of the matrix is a standard Youn
Externí odkaz:
http://arxiv.org/abs/2302.09194
Autor:
Ganguly, Ankan, McDonough, Alex
We make precise and prove a conjecture of Klivans about actions of the sandpile group on spanning trees. More specifically, the conjecture states that there exists a unique ``suitably nice'' sandpile torsor structure on plane graphs which is induced
Externí odkaz:
http://arxiv.org/abs/2203.15079
Autor:
McDonough, Alex
Publikováno v:
Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 795-822
For a natural class of $r \times n$ integer matrices, we construct a non-convex polytope which periodically tiles $\mathbb R^n$. From this tiling, we provide a family of geometrically meaningful maps from a generalized sandpile group to a set of gene
Externí odkaz:
http://arxiv.org/abs/2007.09501
A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa showed that mat
Externí odkaz:
http://arxiv.org/abs/1905.10560
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Autor:
McDonough, Alex
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 23 no. 1, Combinatorics (January 7, 2021) dmtcs:6176
We provide a pair of ribbon graphs that have the same rotor routing and Bernardi sandpile torsors, but different topological genus. This resolves a question posed by M. Chan [Cha]. We also show that if we are given a graph, but not its ribbon structu
Externí odkaz:
http://arxiv.org/abs/1804.07807