A Kruskal–Katona type result and applications

A Kruskal–Katona type result and applications

Inspired by the Kruskal–Katona theorem a minimization problem is studied, where the role of the shadow is replaced by the image of the action of a certain subset of the monoid of increasing functions. One of our main results shows that compressed sets are a solution to this problem. Several applicat...

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Veröffentlicht in:Discrete mathematics 2020-05, Vol.343 (5), p.111801, Article 111801
Hauptverfasser: Le, Dinh Van, Römer, Tim
Format: Artikel
Sprache:eng
Schlagworte:
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Compression
Kruskal–Katona theorem
Monoid action
Simplicial complex
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Zusammenfassung:Inspired by the Kruskal–Katona theorem a minimization problem is studied, where the role of the shadow is replaced by the image of the action of a certain subset of the monoid of increasing functions. One of our main results shows that compressed sets are a solution to this problem. Several applications to simplicial complexes are discussed.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.111801