English

Hyperwalk Formulae for Even and Odd Laplacians in Finite CW-Hypergraphs

Mathematical Physics 2017-08-29 v1 Combinatorics math.MP

Abstract

In this note we provide a combinatorial interpretation for the powers of the hypergraph Laplacians. Our motivation comes from the discrete formulation of quantum mechanics and thermodynamics in the case of finite graphs, which suggest a natural extension to simplicial and CW-complexes. With this motivation, we also define generalizations of the odd Laplacian which is specific to hypergraphs arising from CW-complexes. We then provide a combinatorial interpretation for the powers of these Laplacians.

Cite

@article{arxiv.1708.07995,
  title  = {Hyperwalk Formulae for Even and Odd Laplacians in Finite CW-Hypergraphs},
  author = {Ivan Contreras and Sarah Loeb and Chengzheng Yu},
  journal= {arXiv preprint arXiv:1708.07995},
  year   = {2017}
}

Comments

8 pages, 1 figure

R2 v1 2026-06-22T21:24:19.063Z