Recent Work on the Extremal Problems of Families of Subsets with a Forbidden Subposet

04/29/2011 - 12:00pm
04/29/2011 - 1:00pm
Wei-Tian Li (University of South Carolina)

The Lubell function of a family F of subsets of [n] = {1, 2, ..., n} is the average number of times that a random full chain meets F. This value provides an upper bound on the size of the family F. Given a finite poset P, a family is P-free if it does not contain P as a subposet. By evaluating the maximum value of the Lubell function of P-free families, Griggs, Li, and Lu obtain the exact sizes of largest P-free families for several diamond-shaped posets P. We will see how to obtain the results in this talk. In addition, we define a notion of a strong ordinal sum for these diamond-shaped posets, and, using the Lubell function, determine the size of the largest families not containing them. Joint work with Jerrold R. Griggs and Linyuan Lu.

Millikan 208 (Pomona College)
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