Journal of Integer Sequences, Vol. 10 (2007), Article 07.3.7

Three Proofs and a Generalization of the Goulden-Litsyn-Shevelev Conjecture on a Sequence Arising in Algebraic Geometry


Brian Drake and Ira M. Gessel
Department of Mathematics
Brandeis University
Waltham, MA 02454
USA

Guoce Xin
Center for Combinatorics
LPMC
Nankai University
Tianjin, 300071
P. R. China

Abstract:

We prove and generalize a conjecture of Goulden, Litsyn, and Shevelev that certain Laurent polynomials related to the solution of a functional equation have only odd negative powers.

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(Concerned with sequences A000311 A033282 A074059 and A075856 .)

Received September 17 2006; revised version received April 10 2007. Published in Journal of Integer Sequences April 10 2007.

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