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pro vyhledávání: '"Martin, Jeremy L."'
Stanley asked whether a tree is determined up to isomorphism by its chromatic symmetric function. We approach Stanley's problem by studying the relationship between the chromatic symmetric function and other invariants. First, we prove Crew's conject
Externí odkaz:
http://arxiv.org/abs/2402.10333
A matroid base polytope is a polytope in which each vertex has 0,1 coordinates and each edge is parallel to a difference of two coordinate vectors. Matroid base polytopes are described combinatorially by integral submodular functions on a boolean lat
Externí odkaz:
http://arxiv.org/abs/2312.02040
A graph can be regarded as an electrical network in which each edge is a resistor. This point of view relates combinatorial quantities, such as the number of spanning trees, to electrical ones such as effective resistance. The second and third author
Externí odkaz:
http://arxiv.org/abs/2206.02182
Autor:
Marshall, Kevin, Martin, Jeremy L.
A \textit{grounded set family} on $I$ is a subset $\mathcal{F}\subseteq2^I$ such that $\emptyset\in\mathcal{F}$. We study a linearized Hopf monoid \textbf{SF} on grounded set families, with restriction and contraction inspired by the corresponding op
Externí odkaz:
http://arxiv.org/abs/2205.05772
Autor:
Hanely, Derek, Martin, Jeremy L., McGinnis, Daniel, Miyata, Dane, Nasr, George D., Vindas-Meléndez, Andrés R., Yin, Mei
We show that the base polytope $P_M$ of any paving matroid $M$ can be systematically obtained from a hypersimplex by slicing off certain subpolytopes, namely base polytopes of lattice path matroids corresponding to panhandle-shaped Ferrers diagrams.
Externí odkaz:
http://arxiv.org/abs/2201.12442
We study pure ordered simplicial complexes (i.e., simplicial complexes with a linear order on their ground sets) from the Hopf-theoretic point of view. We define a \textit{Hopf class} to be a family of pure ordered simplicial complexes that give rise
Externí odkaz:
http://arxiv.org/abs/2011.14955
Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair $(a,b)$, where $a$ is a parking fu
Externí odkaz:
http://arxiv.org/abs/2006.09321
Autor:
Adeniran, Ayomikun, Butler, Steve, Dorpalen-Barry, Galen, Harris, Pamela E., Hettle, Cyrus, Liang, Qingzhong, Martin, Jeremy L., Nam, Hayan
Publikováno v:
Electron. J. Combin. 27(2) (2020), #P2.44
Given a strictly increasing sequence $\mathbf{t}$ with entries from $[n]:=\{1,\ldots,n\}$, a parking completion is a sequence $\mathbf{c}$ with $|\mathbf{t}|+|\mathbf{c}|=n$ and $|\{t\in \mathbf{t}\mid t\le i\}|+|\{c\in \mathbf{c}\mid c\le i\}|\ge i$
Externí odkaz:
http://arxiv.org/abs/1912.01688
Akademický článek
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Autor:
Dorpalen-Barry, Galen, Hettle, Cyrus, Livingston, David C., Martin, Jeremy L., Nasr, George, Vega, Julianne, Whitlatch, Hays
Publikováno v:
J. Combin. Theory Ser. A 179 (2021) 105364
Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideration of numerical graph invariants which we call \emph{Elser numbers} $\m
Externí odkaz:
http://arxiv.org/abs/1905.11330