An Integer Sequence Motivated by Generalized Quadrangles
Brian G. Kronenthal
Department of Mathematics
Kutztown University of Pennsylvania
15200 Kutztown Road
Kutztown, PA 19530-9335
In this paper, we prove a closed form for a sequence motivated by the search for new generalized quadrangles of odd order. We present two proofs: a direct proof to explain the closed form’s derivation and a shorter inductive argument. The sequence in question is derived from congruences that arise from applying the Hermite-Dickson criterion to a permutation polynomial that is related to the girth of monomial graphs.
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(Concerned with sequences
Received February 10 2015; revised versions received July 10 2015.
Published in Journal of Integer Sequences, July 16 2015.
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