arXiv math/06090712006-09-03math.CO

关于algebraic geometry中产生序列的Goulden-Litsyn-Shevelev猜想的三种证明

Three proofs of the Goulden-Litsyn-Shevelev conjecture on a sequence arising in algebraic geometry

Brian Drake, Ira M. Gessel, Guoce Xin

备注：: 10 pages
发表信息：: Three proofs and a generalization of the Goulden-Litsyn-Shevelev conjecture on a sequence arising in algebraic geometry, J. Integer Seq. 10 (2007), Article 07.3.7

摘要：

I. P. Goulden，S. Litsyn和V. Shevelev [On a sequence arising in algebraic geometry，J. J. Sequences 8（2005），05.4.7]证明了与函数方程的解相关联的某些Laurent多项式仅具有奇数负幂。我们证明了他们的猜想并推广了它。

英文摘要：

I. P. Goulden, S. Litsyn, and V. Shevelev [On a sequence arising in algebraic geometry, J. Integer Sequences 8 (2005), 05.4.7] conjectured that certain Laurent polynomials associated with the solution of a functional equation have only odd negative powers. We prove their conjecture and generalize it.

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