Combinatorics Seminar
Ameerah Chowdhuri
Carnegie-Mellon
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 $S \subset V$ to be the sum of the weights of all the $1$-dimensional subspaces it contains. We prove that if $n \geq 3k$, 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).
Wednesday February 5, 2014 at 3:00 PM in SEO 427