English

enumeration of weighted paths on a digraph and block hook determinant

Combinatorics 2019-12-04 v1

Abstract

In this article, we evaluate determinants of block hook matrices, which are block matrices consist of hook matrices. In particular, we deduce that the determinant of a block hook matrix factorizes nicely. In addition we give a combinatorial interpretation of the aforesaid factorization property by counting weighted paths in a suitable weighted digraph.

Keywords

Cite

@article{arxiv.1912.01338,
  title  = {enumeration of weighted paths on a digraph and block hook determinant},
  author = {Sudip Bera},
  journal= {arXiv preprint arXiv:1912.01338},
  year   = {2019}
}

Comments

18 pages,6 figures

R2 v1 2026-06-23T12:34:14.767Z