偶特征有限正交空间中格的秩生成函数和Poincaré多项式  

Rank-generating Functions and Poincar´e Polynomials of Lattice in Finite Orthogonal Space of Even Characteristic

作　　者：徐峰[1] 赵燕冰[2] 霍元极[3] XU Feng;ZHAO Yanbing;HUO Yuanji(Office of Academic Affairs,Xuanhua Vocational College of Science and Technology,Zhangjiakou,Hebei,075100,P.R.China;Department of Basic Courses,Zhangjiakou Vocational and Technical College,Zhangjiakou,Hebei,075051,P.R.China;Department of Mathematics,Hebei North Uni-versity,Zhangjiakou,Hebei,075000,P.R.China)

机构地区：[1]宣化科技职业学院教务处,河北张家口075100 [2]张家口职业技术学院基础部,河北张家口075051 [3]河北北方学院数学系,河北张家口075000

出　　处：《数学进展》2024年第2期250-256,共7页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11971146)。

摘　　要：有限域上典型群的几何学在许多领域有着广泛的应用,本文研究在偶特征有限正交群作用下子空间轨道生成格的秩生成函数、特征多项式和Poincaré多项式,并且确定了它们的表示式.The geometry of classical groups over finite fields is widely used in many fields.In this paper,we study the rank-generating function,the characteristic polynomial and the Poincar´e polynomial of lattice generated by the orbits of subspace under geometry of orthogonal group of even characteristic.We also determine their expressions.

关 键 词：格 偶特征正交空间 秩生成函数 特征多项式 Poincaré多项式 

分 类 号：O152.8[理学—数学]