Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/23502
Title: 
Authors: 
Subjects: 
Kruskal-Katona
Sperner families
Antichains
Sperner operations
Cross-intersecting
Issue Date: 
2022
Citation: 
Wong, H. W., & Tay, E. G. (2022). Kruskal-katona function and variants of cross-intersecting antichains. Discrete Mathematics, 345(3), Article 112709. https://doi.org/10.1016/j.disc.2021.112709
Journal: 
Discrete Mathematics
Abstract: 
We prove some properties of the Kruskal-Katona function and apply to the following variant of cross-intersecting antichains. Let n ≥ 4 be an even integer and A and B be two cross-intersecting antichains on [n] with at most k disjoint pairs, i.e., for all Ai ∈ A , Bj ∈ B, Ai ∩ Bj = ∅ only if i = j ≤ k. We prove a best possible upper bound on |A |+|B| and show that the extremal families contain only n2 and (n2+1)-sets. The main tools are Sperner operations and Kruskal-Katona’s Theorem.
URI: 
ISSN: 
0012-365X
DOI: 
Appears in Collections:Journal Articles

Files in This Item:
File Description SizeFormat 
DM-345-3-112709.pdf
  Until 2024-04-01
418.37 kBAdobe PDFUnder embargo until Apr 01, 2024
Show full item record

Page view(s)

21
checked on Jan 20, 2022

Download(s)

1
checked on Jan 20, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.