First distribution invariants and EKR theorems

Manickam, N. ; Singhi, N. M. (1988) First distribution invariants and EKR theorems Journal of Combinatorial Theory - Series A, 48 (1). pp. 91-103. ISSN 0097-3165

Full text not available from this repository.

Official URL:

Related URL:


It is shown by a simple counting argument that, in a projective space Pn−1, any set of [(n−1)/(d−1)] distinct (d−1)-subspaces of Pn−1, d|n, contains a d-spread. A weight function on Pn−1, is a real-valued function on the set In of points of Pn−1 such that the sum of the values on all points of In is nonnegative. The weight of any subset of In is the sum of the weights of all the points in it. It is shown that the number of (d−1)-subspaces in Pn−1 with nonnegative weights is at least [(n−1)/(d−1)]. The case of equality is characterized by using the Erdös-Ko-Rado theorem. These results are then applied to study the first distribution invariant of Jq(n, d). Analogues of these results are proved for sets and affine spaces when n≥2d. In the case of affine spaces the problem is essentially solved.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:50420
Deposited On:23 Jul 2011 11:08
Last Modified:23 Jul 2011 11:08

Repository Staff Only: item control page