Rank-generating functions and Poincaré polynomials of lattices in finite orthogonal space of even characteristic

doi:10.3868/s140-DDD-024-0011-x

Front. Math. China

2024, Vol. 19

Issue (4) : 181-189 https://doi.org/10.3868/s140-DDD-024-0011-x

Rank-generating functions and Poincaré polynomials of lattices in finite orthogonal space of even characteristic

Feng XU¹, Yanbing ZHAO², Yuanji HUO³(

)

¹. Office of Academic Affairs, Xuanhua Vocational College of Science and Technology, Zhangjiakou 075100, China
². Department of Basic Courses, Zhangjiakou Vocational and Technical College, Zhangjiakou 075051, China
³. Department of Mathematics, Hebei North University, Zhangjiakou 075000, China

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Abstract

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 Poincaré polynomial of lattices generated by the orbits of subspaces under finite orthogonal groups of even characteristic. We also determine their expressions.

Keywords Lattices orthogonal space of even characteristic rank-generating function characteristic polynomial Poincaré polynomial

Corresponding Author(s): Yuanji HUO

Online First Date: 25 July 2024 Issue Date: 06 August 2024

Cite this article:

Feng XU,Yanbing ZHAO,Yuanji HUO. Rank-generating functions and Poincaré polynomials of lattices in finite orthogonal space of even characteristic[J]. Front. Math. China, 2024, 19(4): 181-189.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-024-0011-x
https://academic.hep.com.cn/fmc/EN/Y2024/V19/I4/181

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