Autor:	Griggs, Jerrold R., Kalinowski, Thomas, Leck, Uwe, Roberts, Ian T., Schmitz, Michael
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics 06A07 (Primary) 05D05 (Secondary)
Druh dokumentu:	Working Paper
Popis:	This is the second in a sequence of three papers investigating the question for which positive integers $m$ there exists a maximal antichain of size $m$ in the Boolean lattice $B_n$ (the power set of $[n]:=\{1,2,\dots,n\}$, ordered by inclusion). In the previous paper we characterized those $m$ between $\binom{n}{\lceil n/2\rceil}-\lceil n/2\rceil^2$ and the maximum size $\binom{n}{\lceil n/2 \rceil}$ that are not sizes of maximal antichains. In this paper we show that all smaller $m$ are sizes of maximal antichains. Comment: This paper has been merged with arXiv:2106.02226
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2106.02230 Zobrazit plný text záznamu View this record from Arxiv