Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T22:31:38.306Z Has data issue: false hasContentIssue false

DETERMINANTS AND PERMANENTS OF POWER MATRICES

Published online by Cambridge University Press:  17 May 2021

RATSIRI SANGUANWONG
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand e-mail: [email protected]
KIJTI RODTES*
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Abstract

Necessary and sufficient conditions for the equality of the determinant and permanent for all powers of a given matrix are provided. The characterisation is based on a condition on merely one power.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chartrand, G., Lesniak, L. and Zhang, P., Graphs and Digraphs, 6th edn (CRC Press, Boca Raton, FL, 2016).Google Scholar
Marcus, M. and Minc, H., ‘On the relation between the determinant and the permanent’, Illinois J. Math. 5 (1961), 376381.CrossRefGoogle Scholar
Marcus, M. and Newman, M., ‘Inequalities for the permanent function’, Ann. of Math. 75(1) (1962), 4762.CrossRefGoogle Scholar
McCuaig, W., ‘Pólya’s permanent problem’, Electron. J. Combin. 11 (2004), R79.CrossRefGoogle Scholar
Pólya, G., ‘Aufgabe 424’, Arch. Math. Phys. 20(3) (1913), 271.Google Scholar
Szegő, G., ‘Losungzu 424’, Arch. Math. Phys. 21 (1913), 291292.Google Scholar