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

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

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