Geodesic
Extremal families for Kruskal-Katona Theorem
Oriol Serra1 ; Lluis Vena Cros2 ; Oriol Serra ; Lluis Vena Cros
1Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
2Department of Applied Mathematics, Charles University, Prague, Czech Republic
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1043-1048 
Oriol Serra; Lluis Vena Cros; Oriol Serra; Lluis Vena Cros. Extremal families for Kruskal-Katona Theorem. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1043-1048. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a106/
@article{AMUC_2019_88_3_a106,
     author = {Oriol Serra and Lluis Vena Cros and Oriol Serra and Lluis Vena Cros},
     title = { Extremal families for {Kruskal-Katona} {Theorem}},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {1043--1048},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a106/}
}
TY  - JOUR
AU  - Oriol Serra
AU  - Lluis Vena Cros
AU  - Oriol Serra
AU  - Lluis Vena Cros
TI  - Extremal families for Kruskal-Katona Theorem
JO  - Acta mathematica Universitatis Comenianae
PY  - 2019
SP  - 1043
EP  - 1048
VL  - 88
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a106/
ID  - AMUC_2019_88_3_a106
ER  - 
%0 Journal Article
%A Oriol Serra
%A Lluis Vena Cros
%A Oriol Serra
%A Lluis Vena Cros
%T Extremal families for Kruskal-Katona Theorem
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 1043-1048
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a106/
%F AMUC_2019_88_3_a106

Voir la notice de l'article provenant de la source Comenius University

Given a set of size $n$ and a positive integer $k, 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.