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
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
to be the sum of the weights of all the 1
-dimensional subspaces it contains. We prove that if n
, then the number of k
-dimensional subspaces in
with nonnegative weight is at least the number of
-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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