Zobrazeno 1 - 10
of 16
pro vyhledávání: '"David Perkinson"'
Autor:
Sam Hopkins, David Perkinson
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AT,..., Iss Proceedings (2014)
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:
https://doaj.org/article/6dd948a62ecd41f295c7e46cec01ae42
Autor:
Gopal Goel, David Perkinson
Publikováno v:
Linear Algebra and its Applications. 567:138-142
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.
4 pages; to appear in Linear Algebra and its Applications; an example is added in
4 pages; to appear in Linear Algebra and its Applications; an example is added in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0b3570b0c0c53147e23f7c71a3844a2
https://doi.org/10.1016/j.laa.2019.01.009
https://doi.org/10.1016/j.laa.2019.01.009
Autor:
Jesse Kim, David Perkinson
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14e119123221c64cb14e26c4d9bfde19
http://arxiv.org/abs/1908.09350
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6b165bd8898a1e52a40a290457082ae
Autor:
Scott Corry, David Perkinson
Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. The resulting theory of divisors on graphs runs in close
Autor:
David Perkinson, Robert M. Guralnick
Publikováno v:
Journal of Combinatorial Theory, Series A. 113(7):1243-1256
Each group G of n × n permutation matrices has a corresponding permutation polytope, P(G) := conv(G) ⊂ Rn × n. We relate the structure of P(G) to the transitivity of G. In particular, we show that if G has t nontrivial orbits, then min{2t, ⌊n/2
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78839137fe53e20e465a720b4b18d0c5
Autor:
David Perkinson, Jeffrey Hood
Publikováno v:
Linear Algebra and its Applications. 381:237-244
We describe a class of facets of the polytope of convex combinations of the collection of even n×n permutation matrices. As a consequence, we prove the conjecture of Brualdi and Liu [J. Combin. Theory Ser. A 57 (1991) 243] that the number of facets
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::290d94058865c67c4267bdf11097bd0a
Autor:
David Perkinson, Darren B. Glass, Qiaoyu Yang, Caryn Werner, Melody Chan, Matthew S. Macauley
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e6f48b288d1277d3c27819ba9cd4a5b
http://arxiv.org/abs/1406.5147
http://arxiv.org/abs/1406.5147
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::03ba07de87ae136896a3542a6faeabd3
http://arxiv.org/abs/1309.2201
http://arxiv.org/abs/1309.2201