Minimal Path and Acyclic Models in the Path Complex

Shing-Tung Yau; Xinxing Tang

Minimal Path and Acyclic Models in the Path Complex

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arxiv 2208.14063 v2 pith:3FBGZNAJ submitted 2022-08-30 math.AT math.CO

Xinxing Tang , Shing-Tung Yau This is my paper · ORCID

classification math.ATmath.CO

keywords pathminimalwillacycliccomplexomegaapplicationscalled

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abstract

In this paper, firstly, we will study the structure of the path complex $(\Omega_*(G;\Z),\partial)$ of a digraph $G$ via the $\Z$-generators of $\Omega_*(G,\Z)$ under strongly regular condition, which is called the minimal path in \cite{HY}. In particular, we will study various examples of the minimal $3$-paths. Secondly, we will show that the supporting sub-digraph of minimal path has acyclic path homologies. Thirdly, we will consider the applications of such an acyclic model.

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Primitive path homology
math.AT 2024-11 conditional novelty 6.0 of 10

Primitive path homology is a new digraph invariant that coincides with GLMY path homology on asymmetric digraphs and differs on symmetric ones.

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