Geodesic
Bivectors over a Finite Field
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 489-490

Voir la notice de l'article provenant de la source Cambridge University Press

Let U be an n -dimensional vector space over a finite field of q elements. The number of elements of Λ2U of each irreducible length is found using the isomorphism of Λ2U with Hn, the space of n x n skew-symmetric matrices, and results due to Carlitz and MacWilliams on the number of skew-symmetric matrices of any given rank.
DOI : 10.4153/CMB-1981-073-8
Mots-clés : 15A75, Grassmann Spaces, Exterior powers 
MacDougall, J. A. Bivectors over a Finite Field. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 489-490. doi: 10.4153/CMB-1981-073-8
@article{10_4153_CMB_1981_073_8,
     author = {MacDougall, J. A.},
     title = {Bivectors over a {Finite} {Field}},
     journal = {Canadian mathematical bulletin},
     pages = {489--490},
     year = {1981},
     volume = {24},
     number = {4},
     doi = {10.4153/CMB-1981-073-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-073-8/}
}
TY  - JOUR
AU  - MacDougall, J. A.
TI  - Bivectors over a Finite Field
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 489
EP  - 490
VL  - 24
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-073-8/
DO  - 10.4153/CMB-1981-073-8
ID  - 10_4153_CMB_1981_073_8
ER  - 
%0 Journal Article
%A MacDougall, J. A.
%T Bivectors over a Finite Field
%J Canadian mathematical bulletin
%D 1981
%P 489-490
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-073-8/
%R 10.4153/CMB-1981-073-8
%F 10_4153_CMB_1981_073_8

[1] 1. Carlitz, L., Representations by Skew Forms in a Finite Field, Arch. Math. V, 1954, p. 19-31. Google Scholar

[2] 2. MacWilliams, J., Orthogonal Matrices over Finite Fields, Amer. Math. Monthl. 76 (1969), 152-164. Google Scholar

[3] 3. Marcus, M. and Westwick, R., Linear Maps on Skew-Symmetric Matrices: The Invariance of the Elementary Symmetric Functions, Pac. Jour. Math. 10 (1960), 917-924. Google Scholar

Cité par Sources :