Please use this identifier to cite or link to this item: `http://hdl.handle.net/10497/23502`
 Title: Kruskal-Katona function and variants of cross-intersecting antichains Authors: Subjects: Kruskal-KatonaSperner familiesAntichainsSperner operationsCross-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 $\frac{n}{2}$ and $\left(\frac{n}{2}+1\right)$-sets. The main tools are Sperner operations and Kruskal-Katona’s Theorem. URI: http://hdl.handle.net/10497/23502 ISSN: 0012-365X DOI: 10.1016/j.disc.2021.112709 File Permission: Embargo_20240401 File Availability: With file 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

#### Page view(s)

77
checked on Oct 2, 2022