Discrete Math Seminar: Ameera Chowdhury

  • Date: 11/26/2013
  • Time: 15:00
Ameera Chowdhury, Carnegie Mellon

University of British Columbia


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


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