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Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology

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arxiv 2110.11206 v2 pith:OYFRDBOS submitted 2021-10-21 math.CO math.ATmath.GN

Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology

Luigi Caputi , Carlo Collari , Sabino Di Trani This is my paper
classification math.CO math.ATmath.GN
keywords cohomologymultipathpathposetcombinatorialgraphsinvestigateposets
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Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath cohomology. In particular, we develop acyclicity criteria, and provide computations of multipath cohomology groups of oriented linear graphs. We further interpret the path poset as the face poset of a simplicial complex, and we investigate realisability problems.

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