Pólya convertibility problem for symmetric matrices

Guterman, Alexander; Dolinar, Gregor; Kuzma, Bojan

doi:10.1134/s0001434612110053

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2019

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“…Szegö's result didn't put an end to this question. In fact, the possibility that the permanent can be converted into the determinant by affixing ± signs is a research topic that remains active until today (see [1,2] or [5] for recent works on this subject). In 1969, Gibson [3] proved that the linear space of lower Hessenberg matrices is a convertible subspace.…”

Section: Introductionmentioning

confidence: 99%

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

Cruz

Inácio²,

Serôdio³

2019

Ars Math. Contemp.

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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.

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