- Title
- Combinatorics of Euclidean Spaces over Finite Fields
- KIAS Author
- Yoo, Semin
- Journal
- ANNALS OF COMBINATORICS, 2024
- Archive
- https://arxiv.org/abs/1910.03482
- Abstract
- The q-binomial coefficients are q-analogues of the binomial coefficients, counting the number of k-dimensional subspaces in then-dimensional vector spaceFnqoverFq.In this paper, we define a Euclidean analogue of q-binomial coefficients as the number ofk-dimensional sub-spaces 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 ofq-binomial coefficients. In addition, we formulate the number of subspaces of other quadratic types and study some related properties