University of Delaware
Discrete Mathematics Seminar

Combinatorial estimates of the size of an image set
Steven Senger
University of Delaware
Tuesday, September 4, 2012
Ewing Hall 336 4.00 - 5.00 pm

ABSTRACT: We present a family of simple combinatorial estimates of the size of the image set of any function, given some information about how often an element in the range has multiple pre-images. These bounds are sharp in some cases. In particular, we get sharper bounds on the size of the image set of a planar function over finite fields. More generally, we get some (weak) estimates related to additive combinatorics, coding theory, and geometric combinatorics. We also relate the tightness of our bounds to triangular numbers.