Zobrazeno 1 - 10
of 50
pro vyhledávání: '"P. Collari"'
We characterise the digraphs for which the multipaths, that is disjoint unions of directed paths, yield a matroid. For such graphs, called MP-digraphs, we prove that the Tutte polynomial of the multipath matroid is related to counting certain digraph
Externí odkaz:
http://arxiv.org/abs/2409.14528
We establish an isomorphism between the 0-degree \"uberhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify the correspondence between these theories by providing examples and
Externí odkaz:
http://arxiv.org/abs/2406.18778
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
Autor:
Collari, Carlo, Lisca, Paolo
We introduce and study strongly invertible Legendrian links in the standard contact three-dimensional space. We establish the equivariant analogs of basic results separately well-known for strongly invertible and Legendrian links, i.e. the existence
Externí odkaz:
http://arxiv.org/abs/2311.07974
Publikováno v:
Proc. Roy. Soc. Edinburgh Sect. A (2023)
We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexes: the $0$-degree \"uberhomology. Consequently, we obtain a combinator
Externí odkaz:
http://arxiv.org/abs/2304.10134
Autor:
Caputi, Luigi, Collari, Carlo
The aim of this paper is to apply the framework, which was developed by Sam and Snowden, to study structural properties of graph homologies, in the spirit of Ramos, Miyata and Proudfoot. Our main results concern the magnitude homology of graphs intro
Externí odkaz:
http://arxiv.org/abs/2302.06525
Autor:
Collari, Carlo
A result of Corfield, Sati, and Schreiber asserts that $\mathfrak{gl}_n$-weight systems associated to the defining representation are quantum states. In this short note we extend this result to all $\mathfrak{gl}_n$-weight systems corresponding to la
Externí odkaz:
http://arxiv.org/abs/2210.05399
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph ${\tt G}$ is the simplicial complex whose faces are the multipaths of ${\tt G}$. We compute the Euler characteristic, and associated generating fu
Externí odkaz:
http://arxiv.org/abs/2208.04656
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs, and focus on their (twisted) cohomology groups. We characterise orien
Externí odkaz:
http://arxiv.org/abs/2203.03476
Publikováno v:
Journal of Pure and Applied Algebra (2023)
\"Uberhomology is a recently defined homology theory for simplicial complexes, which yields subtle information on graphs. We prove that bold homology, a certain specialisation of \"uberhomology, is related to dominating sets in graphs. To this end, w
Externí odkaz:
http://arxiv.org/abs/2201.00721