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Symmetric Function, Stable Equivalence and Smith Normal Form

2017/12/11 10:29  点击:[]

时间:2017.12.13(周三)9:00-10:00


地点:理科楼LA106


摘要:In the study of determinant formulas for Schur functions, Hamel and Goulden introduced a class of Giambelli-type matrices with respect to outside decompositions of partition diagrams, which unify the Jacobi-Trudi matrices, the Giambelli matrices and the Lascoux-Pragacz matrices. Stanley determined the Smith normal form of a specialized Jacobi-Trudi matrix. Motivated by Stanley’s work, we obtain the Smith normal form of a specialized Giambelli matrix and a specialized Lascoux-Pragacz matrix. Furthermore, we show that, for a given partition, the Smith normal form of any specialized Giambelli type matrix can be obtained from that of the corresponding specialization of the classical Giambelli matrix by a sequence of stabilization operations.


报告人简介:杨立波,南开大学教授,博士生导师, 国家自然科学基金优秀青年基金获得者,2011年入选教育部新世纪优秀人才。现任南开大学组合数学中心副主任。现为中文《数学进展》编委、天津市工业与应用数学学会常务理事、中国运筹学会图论组合分会常务理事。主要从事组合数学方面的研究,在对称函数理论和组合序列的单峰性、实零点理论等方面取得多项重要成果,在《Trans. Amer. Math. Soc.》、 《Intern. Math. Res. Notices》、 《J. Combinatorial Theory Series, A》等权威数学期刊发表论文20余篇。


学院联系人:傅士硕


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