منابع مشابه
Some p-Ranks Related to Orthogonal Spaces*
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, pe) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in O10(2e), O10(3e), O9(5e), O12(5e) and O12(7e). We also give slightly weaker bounds for more general finite classical polar spaces. Another applic...
متن کاملSome p-ranks Related to Hermitian Varieties
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to [2], in which Blokhuis and this author derive the analogous p-ranks for quadrics.
متن کاملBG-Ranks and 2-Cores
We find the number of partitions of n whose BG-rank is j, in terms of pp(n), the number of pairs of partitions whose total number of cells is n, giving both bijective and generating function proofs. Next we find congruences mod 5 for pp(n), and then we use these to give a new proof of a refined system of congruences for p(n) that was found by Berkovich and Garvan.
متن کاملRecent results on p - ranks and Smith normal forms of some 2 − ( v , k , λ ) designs
We survey recent results on p-ranks and Smith normal forms of some 2 − (v, k, λ) designs. In particular, we give a description of the recent work in [11] on the Smith normal forms of the 2-designs arising from projective and affine spaces over Fq .
متن کاملSwitched symplectic graphs and their 2-ranks
We apply Godsil–McKay switching to the symplectic graphs over F2 with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graphwith parameters (22ν−1, 22ν−1, 22ν−2, 22ν−2) and 2-rank 2ν+2 when ν ≥ 3. For the symplectic graph on 63 vertices we investigate repeated switching b...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90533-l