 
Summary: Another 3Part Sperner Theorem
Karen Meagher
Department of Combinatorics and Optimization
University of Waterloo, Waterloo, Ontario, Canada
kmeagher@math.uwaterloo.ca
Submitted: ?? ; Accepted: ?? ;
Mathematics Subject Classifications: 05D05
Abstract
1 Introduction
In this paper, we prove a higher order Sperner theorem.These theorems are stated after
some notation and background results are introduced.
For i, j positive integers with i j, let [i, j] denote the set {i, i + 1, . . . , j}. For k, n
positive integers, set [n]
k
= {A [1, n] : A = k}. A system A of subsets of [1, n] is said
to be kset system if A [n]
k
.
Two subsets A, B are incomparable if A B and B A. A set system on an nset A
is said to be a Sperner set system, if any two distinct sets in A are incomparable.
