Boise Algebra, Geometry, and Combinatorics seminar, October 2018

Abstract: A set A splits an even-sized set B if A contains exactly half the elements of B. For a natural number k, a splitting family on k is a collection of sets that splits any even-sized subset of {1,…,k}. Variations on the concept of splitting families have appeared in applications of combinatorial search. We investigate the number of sets needed to make a splitting family on k. We give some examples and computational results, as well as theoretical partial results identifying the exact number under certain assumptions. This represents a portion of the work from the Summer 2018 REU CAD, with Bryce Frederickson, Sam Mathers, and Hao-Tong Yan.