Periodicity and parity theorems for a statistic on $r$-mino arrangements
J. Integer Seq. 9(3), Article 06.3.6, 18 p., electronic only (2006)
Summary
Summary: We study polynomial generalizations of the $r$-Fibonacci and $r$-Lucas sequences which arise in connection with a certain statistic on linear and circular $r$-mino arrangements, respectively. By considering special values of these polynomials, we derive periodicity and parity theorems for this statistic on the respective structures.
Mathematics Subject Classification
11B39, 05A15
Keywords/Phrases
r-mino arrangement, polynomial generalization, Fibonacci numbers, Lucas numbers
