## Discrete Math Seminar: Ameera Chowdhury

• Date: 11/26/2013
• Time: 15:00
Lecturer(s):
Ameera Chowdhury, Carnegie Mellon
Location:

University of British Columbia

Topic:

A Proof of the Manickam-Miklos-Singhi Conjecture for Vector Spaces

Description:

Abstract: Let V be an n-dimensional vector space over a finite field. Assign a real-valued weight to each 1-dimensional subspace in V so that the sum of all weights is zero. Define the weight of a subspace S of V to be the sum of the weights of all the 1-dimensional subspaces it contains. We prove that if n >= 3k, then the number of k-dimensional subspaces in V with nonnegative weight is at least the number of k-dimensional subspaces in V that contain a fixed 1-dimensional subspace. This result verifies a conjecture of Manickam and Singhi from 1988.

Joint work with Ghassan Sarkis (Pomona College) and Shahriar Shahriari (Pomona College).

Other Information:

Location: ESB 4133