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The Alon-Jaeger-Tarsi Conjecture

March 06, 2019, 12:15 PM - 1:15 PM

Location:

Mathematics Graduate Student Lounge -- 7th Floor

Rutgers University

Hill Center

Mathematics Department

110 Frelinghuysen Road

Piscataway, NJ 08854

Aditi Dudeja, Rutgers University

The Alon-Jaeger-Tarsi conjecture states that for any field F with |F|geq 4 and any non-singular matrix A over F, there is a vector x such that both x and Ax have only non-zero entries. I will relate this conjecture to the perrank of a matrix A which is the size of the largest square submatrix of A with non-zero permanent. I will state and prove some properties of perrank, and use these to prove a small result on the Alon-Jaeger-Tarsi conjecture.