A Residue Theorem for Malcev-Neumann Series
组合数学
2007-05-23 v2 交换代数
摘要
In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal series that are related by a change of variables. We obtain simple conditions for when a change of variables is possible, and find that the two related formal series in fact belong to two different fields of Malcev-Neumann series. The multivariate Lagrange inversion formula is easily derived and Dyson's conjecture is given a new proof and generalized.
引用
@article{arxiv.math/0409190,
title = {A Residue Theorem for Malcev-Neumann Series},
author = {Guoce Xin},
journal= {arXiv preprint arXiv:math/0409190},
year = {2007}
}
备注
22 pages, extensive revision