The Increasing Families of Sets Generated by Self-dual Clutters

Abstract

Using the KKS inequalities, we establish bounds on the numbers of $k$-sets in the increasing families generated by self-dual clutters (i.e., clutters $\mathcal{A}$ that coincide with the blockers $\mathfrak{B}(\mathcal{A})$) on their ground set of even cardinality.

14 pages

References in corpus (2)

• Combinatorial Alexander Duality -- a Short and Elementary Proof
• Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs