Convertible subspaces that arise from different numberings of the vertices of a graph

Henrique F. da Cruz, Ilda Inácio, Rogério Serôdio

Abstract


In this paper, we describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. These subspaces can arise from different numberings of the vertices of a graph. With this numbering process, we obtain some well-known sequences of integers. For instance, in the case of a path of length n, we prove that the number of these subspaces is the (n + 1)th Fibonacci number.

Keywords


Determinant, permanent, Hessenberg matrix

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DOI: https://doi.org/10.26493/1855-3974.1477.1c7

ISSN: 1855-3974

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