Geodesic
Parity theorems for statistics on domino arrangements
The electronic journal of combinatorics, Tome 12 (2005)
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We study special values of Carlitz's $q$-Fibonacci and $q$-Lucas polynomials $F_n(q,t)$ and $L_n(q,t)$. Brief algebraic and detailed combinatorial treatments are presented, the latter based on the fact that these polynomials are bivariate generating functions for a pair of statistics defined, respectively, on linear and circular domino arrangements.
DOI : 10.37236/1977
Classification : 05A15, 11B39
Mots-clés : special values of Carlitz's \(q\)-Fibonacci and \(q\)-Lucas polynomials, bivariate generating functions, linear and circular domino arrangements 
@article{10_37236_1977,
     author = {Mark A. Shattuck and Carl G. Wagner},
     title = {Parity theorems for statistics on domino arrangements},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1977},
     zbl = {1074.05010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1977/}
}
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%A Carl G. Wagner
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Mark A. Shattuck; Carl G. Wagner. Parity theorems for statistics on domino arrangements. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1977

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