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