A Combinatorial Approach to Fibonomial Coefficients

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Sean S. Plott '08, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2-2008

Abstract

A combinatorial argument is used to explain the integrality of Fibonomial coefficients and their generalizations. The numerator of the Fibonomial coeffcient counts tilings of staggered lengths, which can be decomposed into a sum of integers, such that each integer is a multiple of the denominator of the Fibonomial coeffcient. By colorizing this argument, we can extend this result from Fibonacci numbers to arbitrary Lucas sequences.

Comments

First published in the Fibonacci Quarterly, vol. 46/47, no. 1 (February 2008/2009), by the Fibonacci Association.

This article is also available at http://www.fq.math.ca/46_47-1.html.

Errata (attached as an additional file) published in the Fibonacci Quarterly, vol 48, no. 3 (August 2010), by the Fibonacci Association.

Rights Information

© 2008/2009 The Fibonacci Association

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Recommended Citation

Benjamin, A.T., & Plott, S.S. (2008/2009). A combinatorial approach to Fibonomial coefficients. Fibonacci Quarterly, 46/47(1): 7-9.