Geodesic
Traces without maximal chains
The electronic journal of combinatorics, Tome 17 (2010)

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The trace of a family of sets ${\cal A}$ on a set $X$ is ${\cal A}|_X=\{A\cap X:A\in {\cal A}\}$. If ${\cal A}$ is a family of $k$-sets from an $n$-set such that for any $r$-subset $X$ the trace ${\cal A}|_X$ does not contain a maximal chain, then how large can ${\cal A}$ be? Patkós conjectured that, for $n$ sufficiently large, the size of ${\cal A}$ is at most ${n-k+r-1\choose r-1}$. Our aim in this paper is to prove this conjecture.
DOI : 10.37236/465
Classification : 05D05 
Ta Sheng Tan. Traces without maximal chains. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/465
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     author = {Ta Sheng Tan},
     title = {Traces without maximal chains},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/465},
     zbl = {1205.05234},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/465/}
}
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