有限格中的秩生成函数和Poincaré多项式  

Rank-generating Functions and PoincaréPolynomials in the Finite Lattices

作　　者：霍元极[1] HUO YUANJI(Department of Mathematics,Hebei North University,Zhangjiakou 075000,China)

机构地区：[1]河北北方学院数学系,张家口075000

出　　处：《应用数学学报》2022年第6期781-794,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11971146)资助项目.

摘　　要：在一些有限格B_(n),D_(n),∏_(n)中,利用组合系数的方法分别给出了它们的秩生成函数和D_(n)的特征多项式.在有限典型群子空间轨道生成的格中,利用典型群理论和计算法给出在GL_(n)(F_(q)^(n)),Sp_(2v)(F_(q)^(n)),Un(F_(q^(2))^(n))作用下子空间轨道生成格的秩生成函数和特征多项式,并且给出这些格的Poincaré多项式的定义,确定了它们的表示式.In the finite lattices B_(n),D_(n),∏_(n) using the method of combinatorial coefficients their rank-generating functions and characteristic polynomial of D_(n) are gievn.In some lattices generated by the orbits of the subspaces under the action of finite classical groups the cases of GL_(n)(F_(q)^(n)),Sp_(2v)(F_(q)^(n)),Un(F_(q^(2))^(n)) using the theory and algorithm of finite classical groups their rank-generating functions and the characteristic polynomials are introduced,the Poincarépolynomial has been defined,and their expressions are also determined.

关 键 词：格 秩生成函数 典型群 特征多项式 Poincaré多项式 

分 类 号：O152.8[理学—数学]