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- W2007473634 abstract "The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: $Asubset B,Csubset D$. A diamond-free family in the $n$-dimensional Boolean lattice is a subposet such that no four elements form a diamond. Note that elements $B$ and $C$ may or may not be related. There is a diamond-free family in the $n$-dimensional Boolean lattice of size $(2-o(1)){nchooselfloor n/2rfloor}$. In this paper, we prove that any diamond-free family in the $n$-dimensional Boolean lattice has size at most $(2.25+o(1)){nchooselfloor n/2rfloor}$. Furthermore, we show that the so-called Lubell function of a diamond-free family in the $n$-dimensional Boolean lattice is at most $2.25+o(1)$, which is asymptotically best possible." @default.
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- W2007473634 date "2013-04-01" @default.
- W2007473634 modified "2023-09-29" @default.
- W2007473634 title "On diamond-free subposets of the Boolean lattice" @default.
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- W2007473634 doi "https://doi.org/10.1016/j.jcta.2012.11.002" @default.
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