Binomial Coefficients and Enumeration of Restricted Words
Department of Mathematics and Informatics
University of Banja Luka
Banja Luka, 78000
Republic of Srpska, Bosnia and Herzegovina
We derive partial solutions for a recently-posed problem of the
enumeration of restricted words. We obtain several explicit formulas in
which the number of restricted words is expressed in terms of the
binomial coefficients. These results establish relations between the
partial Bell polynomials and the binomial coefficients.
In particular, we link the r-step Fibonacci numbers, the binomial
coefficients, and the partitions of a positive integer into at most r
parts. Also, we prove that several well-known classes of integers can
be interpreted in terms of compositions. We finish the paper with an
extension of a recent result about Euler-type identities for integer
Full version: pdf,
(Concerned with sequences
Received January 7 2016; revised versions received June 13 2016; June 28 2016; July 10 2016.
Published in Journal of Integer Sequences,
August 29 2016.
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