Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.1

Parity Theorems for Statistics on Lattice Paths and Laguerre Configurations


Mark A. Shattuck and Carl G. Wagner
Mathematics Department
University of Tennessee
Knoxville, TN 37996-1300
USA

Abstract: 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.

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(Concerned with sequences A000262 and A089656 .)

Received July 1 2005; revised version received October 18 2005. Published in Journal of Integer Sequences October 20 2005.

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