Abstract
Let V be an ndimensional vector space over a finite field. Assign a realvalued weight to each 1dimensional subspace in V so that the sum of all weights is zero. Define the weight of any other subspace of V to be the sum of the weights of all the 1dimensional subspaces it contains. What is the minimum possible number of kdimensional subspaces of V with nonnegative weight? Together with Ameera Chowdhury and Ghassan Sarkis, we prove that if n >= 3k, then this number is no less than the number of kdimensional subspaces in V that contain a fixed 1dimensional subspace. This result verifies a conjecture of Manickam and Singhi from 1988. The talk will discuss this conjecture and its proof as well as the related conjecture and results in the Boolean Lattices.
Information:
Date:  Thursday, December 26, 2013 at 11:0012:00
 Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
