Discrete Math Seminar: Ameera Chowdhury

  • Date: 11/19/2013
  • Time: 14:30
Ameera Chowdhury

Simon Fraser University


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


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  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).

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Location: K9509