r-Cross t-intersecting families via necessary intersection points

Publikationstyp
Journal Article
Date Issued
2023-02-20
Sprache
English
Author(s)
Gupta, Pranshu  
Mogge, Yannick  
Piga, Simón  
Schülke, Bjarne  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/15075
Journal
Bulletin of the London Mathematical Society  
Volume
55
Issue
3
Start Page
1447
End Page
1458
Citation
Bulletin of the London Mathematical Society 55(3): 1447-1458 (2023)
Publisher DOI
10.1112/blms.12803
Scopus ID
2-s2.0-85148519611
Publisher
Wiley
Given integers (Formula presented.) and (Formula presented.) we call families (Formula presented.) (Formula presented.) -cross (Formula presented.) -intersecting if for all (Formula presented.), (Formula presented.), we have (Formula presented.). We obtain a strong generalisation of the classic Hilton–Milner theorem on cross-intersecting families. In particular, we determine the maximum of (Formula presented.) for (Formula presented.) -cross (Formula presented.) -intersecting families in the cases when these are (Formula presented.) -uniform families or arbitrary subfamilies of (Formula presented.). Only some special cases of these results had been proved before. We obtain the aforementioned theorems as instances of a more general result that considers measures of (Formula presented.) -cross (Formula presented.) -intersecting families. This also provides the maximum of (Formula presented.) for families of possibly mixed uniformities (Formula presented.).
DDC Class
510: Mathematics
Publication version
acceptedVersion
Lizenz
https://creativecommons.org/licenses/by-nc-nd/4.0/
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