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 .

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Received September 4, 1997

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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

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