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pro vyhledávání: '"Ramos, Eric A."'
Some of the most classically relevant Hyperplane arrangements are the Braid Arrangements $B_n$ and their associated compliment spaces $\mathcal{F}_n$. In their recent work, Tsilevich, Vershik, and Yuzvinsky construct what they refer to as the intrins
Externí odkaz:
http://arxiv.org/abs/2405.13291
Autor:
Guan, David, Ramos, Eric
FI-graphs were introduced by the second author and White to capture the idea of a family of nested graphs, each member of which is acted on by a progressively larger symmetric group. That work was built on the newly minted foundations of representati
Externí odkaz:
http://arxiv.org/abs/2401.16739
Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to quivers. As case of study, we investigate the consequences on the homo
Externí odkaz:
http://arxiv.org/abs/2401.01248
We compute the homology of the matching complex $M(\Gamma)$, where $\Gamma$ is the complete hypergraph on $n\geq 2$ vertices, and analyse the $S_n$-representations carried by this homology. These results are achieved using standard techniques in comb
Externí odkaz:
http://arxiv.org/abs/2312.13750
Autor:
Knudsen, Ben, Ramos, Eric
We formulate a categorification of Robertson's conjecture analogous to the categorical graph minor conjecture of Miyata--Proudfood--Ramos. We show that these conjectures imply the existence of a finite list of atomic graphs generating the homology of
Externí odkaz:
http://arxiv.org/abs/2305.19363
Autor:
Ramos, Eric, White, Graham
Publikováno v:
In Linear Algebra and Its Applications 15 October 2024 699:277-294
Autor:
Ramos, Eric, White, Graham
For each $n,r \geq 0$, let $KG(n,r)$ denote the Kneser Graph; that whose vertices are labeled by $r$-element subsets of $n$, and whose edges indicate that the corresponding subsets are disjoint. Fixing $r$ and allowing $n$ to vary, one obtains a fami
Externí odkaz:
http://arxiv.org/abs/2109.10281
We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case
Externí odkaz:
http://arxiv.org/abs/2104.00715
Autor:
Miyata, Dane, Ramos, Eric
We study a variety of natural constructions from topological combinatorics, including matching complexes as well as other graph complexes, from the perspective of the graph minor category of \parencite{MiProRa}. We prove that these complexes must hav
Externí odkaz:
http://arxiv.org/abs/2012.01679
Autor:
Ramos, Eric, Proudfoot, Nicholas
We prove that the ith graded pieces of the Orlik-Solomon algebras or Cordovil algebras of resonance arrangements form a finitely generated FS^op-module, thus obtaining information about the growth of their dimensions and restrictions on the irreducib
Externí odkaz:
http://arxiv.org/abs/2011.01323