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

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0097-3165(88)90077-5

## Abstract

It is shown by a simple counting argument that, in a projective space P_{n−1}, any set of [(n−1)/(d−1)] distinct (d−1)-subspaces of P_{n−1}, d|n, contains a d-spread. A weight function on P_{n−1}, is a real-valued function on the set In of points of P_{n−1} such that the sum of the values on all points of I_{n} is nonnegative. The weight of any subset of I_{n} is the sum of the weights of all the points in it. It is shown that the number of (d−1)-subspaces in P_{n−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 J_{q}(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.

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Deposited On: | 23 Jul 2011 11:08 |

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