Geodesic
Periodicity and parity theorems for a statistic on \(r\)-mino arrangements
Journal of integer sequences, Tome 9 (2006) no. 3
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.
Classification : 11B39, 05A15
Keywords: r-mino arrangement, polynomial generalization, Fibonacci numbers, Lucas numbers 
@article{JIS_2006__9_3_a7,
     author = {Shattuck,  Mark A. and Wagner,  Carl G.},
     title = {Periodicity and parity theorems for a statistic on \(r\)-mino arrangements},
     journal = {Journal of integer sequences},
     year = {2006},
     volume = {9},
     number = {3},
     zbl = {1178.11017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_3_a7/}
}
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Shattuck,  Mark A.; Wagner,  Carl G. Periodicity and parity theorems for a statistic on \(r\)-mino arrangements. Journal of integer sequences, Tome 9 (2006) no. 3. http://geodesic.mathdoc.fr/item/JIS_2006__9_3_a7/