ACO The ACO Seminar (2013–2014)

Oct. 31, 3:30pm, Wean 8220
Ameerah Chowdhury, Carnegie Mellon University
A proof of the Manickam–Miklós–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 of V to be the sum of the weights of all the 1-dimensional subspaces it contains. We prove that if n3k, 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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