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学术报告会:Algorithmic development for MacMahon's partition analysis

2024年09月19日 17:29  点击:[]

报告题目:Algorithmic development for MacMahon's partition analysis

人: 辛国策(首都师范大学   教授)

报告时间:2024923日周一10:00

腾讯会议ID:424-589-781


Abstract: Solutions to a linear Diophantine system, or lattice points in a rational convex polytope, are important concepts in algebraic combinatorics and computational geometry. The enumeration problem isfundamental and has been well studied, because it has many applications in various fields of mathematics.

In computational geometry, Barvinok's  important result asserts the existence of a polynomial algorithm when the dimension is fixed. In algebraic combinatorics, MacMahon partition analysis has become a general approach for linear Diophantine system related problems. The core problem is to compute the constant term of an Elliott-rational function, which is a rational function whose denominator is a product of binomials.


个人简介:

辛国策,首都师范大学数学科学学院教授。主要从事计数组合学和代数组合学方向的研究,已在《J. Combin. Theory Ser. A》、《Int. Math. Res. Not. IMRN》、《Adv. in Appl. Math.》、《J. Symbolic Comput.》等国际学术期刊发表文章50余篇,涉及线性丢番图方程,格路计数,行列式计算等。发展了以迭代Laurent级数域为基础的部分分式法,该方法在常数项计算,分拆理论,对称函数论等方向有广泛的应用,得到了国内外同行的高度评价。特别是美国数学会Steele重大贡献奖和ICAs Euler奖获得者Doron Zeilberger评价其算法为“卓越的”此外,在代数组合领域做出了一系列有影响的工作,尤其是在Shuffle猜想方面的一篇文章中,创造性地将代数几何中的有理型Shuffle 猜想引入代数组合中,并推广到非互素的情形,是递归证明有理型Shuffle 猜想的基础,它推进了Shuffle猜想的研究,得到了国内外同行广泛的关注。



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