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- W2574686372 abstract "In this paper, we study the following classical question of extremal set theory: what is the maximum size of a family of subsets of $[n]$ such that no $s$ sets from the family are pairwise disjoint? This problem was first posed by ErdH os and resolved for $nequiv 0, -1 (mathrm{mod } s)$ by Kleitman in the 60s. Very little progress was made on the problem until recently. The only result was a very lengthy resolution of the case $s=3, nequiv 1 (mathrm{mod } 3)$ by Quinn, which was written in his PhD thesis and never published in a refereed journal. In this paper, we give another, much shorter proof of Quinn's result, as well as resolve the case $s=4, nequiv 2 (mathrm{mod } 4)$. This complements the results in our recent paper, where, in particular, we answered the question in the case $nequiv -2 (mathrm{mod } s)$ for $sge 5$." @default.
- W2574686372 created "2017-01-26" @default.
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- W2574686372 date "2017-01-15" @default.
- W2574686372 modified "2023-09-27" @default.
- W2574686372 title "Families of sets with no matchings of sizes 3 and 4" @default.
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