On characteristic and permanent polynomials of a matrix

• Autorzy: Ranveer Singh , R. B. Bapat
• Języki publikacji: EN

Abstrakty

EN

There is a digraph corresponding to every square matrix over ℂ. We generate a recurrence relation using the Laplace expansion to calculate the characteristic and the permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic and the permanent polynomials can be calculated in terms of the characteristic and the permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Similar to the characteristic and the permanent polynomials; the determinant and the permanent can also be calculated. Therefore, this article provides a combinatorial meaning of these useful quantities of the matrix theory. We conclude this article with a number of open problems which may be attempted for further research in this direction.

Słowa kluczowe

EN

Determinant; Permanent; Block; Block Graph; ℬ-partition

Kategorie tematyczne

• 15A15: Determinants, permanents, other special matrix functions
• 68R10: Graph theory (including graph drawing)
• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 97-112

Daty

wydano

2017-01-26

otrzymano

2017-01-31

zaakceptowano

2017-05-16

online

2017-07-01

Twórcy

autor

Ranveer Singh

• ,

autor

R. B. Bapat

• - 110 016,

Identyfikatory

DOI

10.1515/spma-2017-0010