On Uniform f-vectors of Cutsets in the Truncated Boolean Lattice

and let be the collection of all subsets of [n] ordered by inclusion. is a cutset if it meets every maximal chain in , and the width of is the minimum number of chains in a chain decomposition of . Fix . What is the smallest value of such that there exists a cutset that consists only of subsets of sizes between m and l, and such that it contains exactly k subsets of size i for each ? The answer, which we denote by , gives a lower estimate for the width of a cutset between levels m and l in . After using the Kruskal–Katona Theorem to give a general characterization of cutsets in terms of the number and sizes of their elements, we find lower and upper bounds (as well as some exact values) for .

This is a preview of subscription content, access via your institution.

Author information



Additional information

Received September 4, 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bajnok, B., Shahriari, S. On Uniform f-vectors of Cutsets in the Truncated Boolean Lattice. Combinatorica 20, 1–14 (2000). https://doi.org/10.1007/PL00009834

Download citation

  • AMS Subject Classification (1991) Classes:  05D05, 06A07, 06E05, 06B05