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

Cruz, Henrique F. Da; Inácio, Ilda; Serôdio, Rogério

http://hdl.handle.net/10400.6/9093

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Authors

Cruz, Henrique F. Da

Inácio, Ilda

Serôdio, Rogério

Abstract(s)

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.