A study on one algebraic equation of the product equaling unit
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O187.2

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    Abstract:

    In this paper, we consider the relationship between the Deligne-Simpson problem and the Hurwitz enumeration problem. First, we observe that they are the solutions of the same algebraic equation on different groups, which the algebraic equation is (A_1,B_1)…(A_g,B_g)X_1…X_k=I. When G is the general linear group over the complex field, this equation is equivalent to Deligne-Simpson problem; When G is the general linear group over the finite field, this equation is equivalent to the Euler characteristic of solution space for Deligne-Simpson problem; When G is the permutation group, the equation is equivalent to the Hurwitz enumeration problem. Then we calculate the Euler characteristic of the 3th order Deligne-Simpson problem with any partition, and we express the generating function of some Euler characteristic as the rational functions.

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Cite this article as: LI Sha-Sha, ZHENG Quan. A study on one algebraic equation of the product equaling unit [J]. J Sichuan Univ: Nat Sci Ed, 2016, 53: 229.

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History
  • Received:May 05,2015
  • Revised:May 21,2015
  • Adopted:June 15,2015
  • Online: November 15,2016