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- Title
Combinatorics of Euclidean Spaces over Finite Fields.
- Authors
Yoo, Semin
- Abstract
The q-binomial coefficients are q-analogues of the binomial coefficients, counting the number of k-dimensional subspaces in the n-dimensional vector space F q n over F q. In this paper, we define a Euclidean analogue of q-binomial coefficients as the number of k-dimensional subspaces which have an orthonormal basis in the quadratic space (F q n , x 1 2 + x 2 2 + ⋯ + x n 2). We prove its various combinatorial properties compared with those of q-binomial coefficients. In addition, we formulate the number of subspaces of other quadratic types and study some related properties.
- Subjects
FINITE fields; COMBINATORICS; VECTOR spaces; ORTHONORMAL basis; QUADRATIC forms
- Publication
Annals of Combinatorics, 2024, Vol 28, Issue 1, p283
- ISSN
0218-0006
- Publication type
Article
- DOI
10.1007/s00026-023-00661-3