Geodesic
Parity theorems for statistics on lattice paths and Laguerre configurations
Journal of integer sequences, Tome 8 (2005) no. 5
We examine the parity of some statistics on lattice paths and Laguerre configurations, giving both algebraic and combinatorial treatments. For the former, we evaluate $q$-generating functions at $q =-1$; for the latter, we define appropriate parity-changing involutions on the associated structures. In addition, we furnish combinatorial proofs for a couple of related recurrences.
Classification : 05A99, 05A10
Keywords: Laguerre configuration, lah numbers, lattice paths, q-binomial coefficient 
@article{JIS_2005__8_5_a1,
     author = {Shattuck,  Mark A. and Wagner,  Carl G.},
     title = {Parity theorems for statistics on lattice paths and {Laguerre} configurations},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {5},
     zbl = {1104.05010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_5_a1/}
}
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Shattuck,  Mark A.; Wagner,  Carl G. Parity theorems for statistics on lattice paths and Laguerre configurations. Journal of integer sequences, Tome 8 (2005) no. 5. http://geodesic.mathdoc.fr/item/JIS_2005__8_5_a1/