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Multipath cohomology is a cohomology theory for directed graphs, which isdefined using the path poset. The aim of this paper is to investigatecombinatorial properties of path posets, and to provide computational tools formultipath cohomology. In particular, we develop acyclicity criteria, andprovide 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.

Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology