Non-overlapping matrices
Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani
TL;DR
This paper introduces a set of non-overlapping binary matrices, provides a formula involving generalized Fibonacci numbers for their enumeration, and shows that their generating function is rational.
Contribution
It offers a new enumeration formula for non-overlapping binary matrices using k-generalized Fibonacci numbers and establishes the rationality of their generating function.
Findings
Enumeration formula involving k-generalized Fibonacci numbers
Rational generating function for the sequence
Defined a set of non-overlapping binary matrices
Abstract
Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the -generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational.
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