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of 51
pro vyhledávání: '"Perkinson, David"'
The totally nonnegative Grassmannian $\mathrm{Gr}(k,n)_{\geq0}$ is the subset of the real Grassmannian $\mathrm{Gr}(k,n)$ consisting of points with all nonnegative Pl\"ucker coordinates. The circular Bruhat order is a poset isomorphic to the face pos
Externí odkaz:
http://arxiv.org/abs/2108.03504
Autor:
Kim, Jesse, Perkinson, David
Publikováno v:
The Electronic Journal of Combinatorics, Volume 29, Issue 2 (2022)
The dollar game is a chip-firing game introduced by Baker and Norine (2007) as a context in which to formulate and prove the Riemann-Roch theorem for graphs. A divisor on a graph is a formal integer sum of vertices. Each determines a dollar game, the
Externí odkaz:
http://arxiv.org/abs/1908.09350
The divisor theory of graphs views a finite connected graph $G$ as a discrete version of a Riemann surface. Divisors on $G$ are formal integral combinations of the vertices of $G$, and linear equivalence of divisors is determined by the discrete Lapl
Externí odkaz:
http://arxiv.org/abs/1906.04768
Publikováno v:
In Journal of Combinatorial Theory, Series A April 2023 195
Autor:
Goel, Gopal, Perkinson, David
Let G be a finite graph, and let G_n be the n-th iterated cone over G. We study the structure of the critical group of G_n arising in divisor and sandpile theory.
Comment: 4 pages; to appear in Linear Algebra and its Applications; an example is
Comment: 4 pages; to appear in Linear Algebra and its Applications; an example is
Externí odkaz:
http://arxiv.org/abs/1809.07379
Autor:
Chan, Melody, Glass, Darren, Macauley, Matthew, Perkinson, David, Werner, Caryn, Yang, Qiaoyu
Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing to define a
Externí odkaz:
http://arxiv.org/abs/1406.5147
We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino til
Externí odkaz:
http://arxiv.org/abs/1406.0100
A depth-first search version of Dhar's burning algorithm is used to give a bijection between the parking functions of a graph and labeled spanning trees, relating the degree of the parking function with the number of inversions of the spanning tree.
Externí odkaz:
http://arxiv.org/abs/1309.2201
Autor:
Goel, Gopal, Perkinson, David
Publikováno v:
In Linear Algebra and Its Applications 15 April 2019 567:138-142
Autor:
Hopkins, Sam, Perkinson, David
Publikováno v:
Transactions of the American Mathematical Society, 368(1), 2016
We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A conseque
Externí odkaz:
http://arxiv.org/abs/1212.4398