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ALTERNATING CIRCULAR SUMS OF BINOMIAL COEFFICIENTS

Part of: Combinatorics Sequences and sets

Published online by Cambridge University Press:  13 April 2022

WENCHANG CHU Open the ORCID record for WENCHANG CHU [Opens in a new window]
WENCHANG CHU*
Affiliation:
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan, PR China Current address: Department of Mathematics and Physics, University of Salento (PO Box 193), 73100 Lecce, Italy
*
e-mail: chu.wenchang@unisalento.it
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Abstract

By combining the generating function approach with the Lagrange expansion formula, we evaluate, in closed form, two multiple alternating sums of binomial coefficients, which can be regarded as alternating counterparts of the circular sum evaluation discovered by Carlitz [‘The characteristic polynomial of a certain matrix of binomial coefficients’, Fibonacci Quart. 3(2) (1965), 81–89].

Keywords

circular sumgenerating functionbinomial coefficientLucas numberFibonacci numberLagrange expansion formula

MSC classification

Primary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
Secondary: 05A15: Exact enumeration problems, generating functions 11B65: Binomial coefficients; factorials; $q$-identities

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 385 - 395
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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