Lattices associated with vector spaces over a finite field

Wang, Kaishun; Li, Zengti

doi:10.1016/j.laa.2008.02.035

Cited by 12 publications

(2 citation statements)

References 7 publications

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“…The results on the lattices generated by one orbit of subspaces under finite classical groups may be found in Gao and You [3], Huo et al [4][5][6], Huo and Wan [7], Orlik and Solomon [8], Wang and Feng [9], Wang and Guo [10], and Wang and Li [11].…”

Section: Introductionmentioning

confidence: 96%

Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

Liu

2013

Journal of Applied Mathematics

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In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” by Wang and Guo. The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic polynomials.

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Section: Introductionmentioning

confidence: 96%

Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

Liu

2013

Journal of Applied Mathematics

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“…The results on the lattices generated by one orbit of subspaces under finite classical groups may be found in Huo, Liu and Wan [4][5][6], Huo and Wan [7], Gao and You [3], Orlik and Solomon [8], Guo and Wang [11], Wang and Feng [10], Wang and Li [12].…”

Section: Introductionmentioning

confidence: 99%

Lattices generated by two orbits of subspaces under finite classical groups

Wang¹,

Guo²

2009

Finite Fields and Their Applications

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Let F (n) q be the n-dimensional vector space over a finite field F q , and let G n be the symplectic group Sp n (F q ) where n = 2ν; or the unitary group U n (F q ) where q = q 2 0 . For any two orbits M 1 and M 2 of subspaces under G n , let L 1 (resp. L 2 ) be the set of all subspaces which are sums (resp. intersections) of subspaces in M 1 (resp. M 2 ) such that M 2 ⊆ L 1 (resp. M 1 ⊆ L 2 ). Suppose L is the intersection of L 1 and L 2 containing {0} and F (n) q . By ordering L by ordinary or reverse inclusion, two families of atomic lattices are obtained. This article characterizes the subspaces in these lattices and classifies their geometricity.

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Lattices Associated with Partial Injective Linear Maps of Finite Vector Spaces

Jiang

Zhang

2014

Advances in Intelligent Systems and Computing

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Lattices associated with vector spaces over a finite field

Cited by 12 publications

References 7 publications

Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

Lattices generated by two orbits of subspaces under finite classical groups

Lattices Associated with Partial Injective Linear Maps of Finite Vector Spaces

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