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MULTINOMIAL VANDERMONDE CONVOLUTION VIA PERMANENT

Part of: Basic linear algebra Combinatorics

Published online by Cambridge University Press:  06 November 2020

KIJTI RODTES Open the ORCID record for KIJTI RODTES [Opens in a new window]
KIJTI RODTES*
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
*
e-mail: kijtir@nu.ac.th
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Abstract

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We provide a generalised Laplace expansion for the permanent function and, as a consequence, we re-prove a multinomial Vandermonde convolution. Some combinatorial identities are derived by applying special matrices to the expansion.

Keywords

derangement numbersLaplace expansionpermanentVandermonde convolution

MSC classification

Primary: 05A19: Combinatorial identities, bijective combinatorics
Secondary: 15A15: Determinants, permanents, other special matrix functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 353 - 361
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

The author thanks the Faculty of Science, Naresuan University, for financial support on project number P2562C033.

References

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Merris, R., Multilinear Algebra (Gordon and Breach Science Publishers, Amsterdam, 1997).CrossRefGoogle Scholar
Sulanke, R. A., ‘A generalized $q$ -multinomial Vandermonde convolution’, J. Combin. Theory Ser. A 31 (1981), 33–42.CrossRefGoogle Scholar
Zeng, J., ‘Multinomial convolution polynomial’, Discrete Math. 160 (1996), 219–228.CrossRefGoogle Scholar