Extremal families for Kruskal-Katona Theorem

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Oriol Serra Lluis Vena Cros


    Given a set of size $n$ and a positive integer $k<n$, Kruskal--Katona theorem gives the minimum size of the shadow of a family $S$ of $k$-sets of $[n]$ in terms of the cardinality of $S$.            We give a characterization of the families of $k$-sets satisfying equality in Kruskal--Katona theorem. This answers a question of F\"uredi and Griggs.

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Serra, O., & Vena Cros, L. (2019). Extremal families for Kruskal-Katona Theorem. Acta Mathematica Universitatis Comenianae, 88(3), 1043-1048. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1301/760