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pro vyhledávání: '"Griggs, Jerrold R."'
This is the second of two papers investigating 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 first part, the sizes of
Externí odkaz:
http://arxiv.org/abs/2302.07062
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
Externí odkaz:
http://arxiv.org/abs/2106.02230
Publikováno v:
Order, Volume 40, pages 537-574, (2023)
Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a maximal antichain of size $m$ in the Boolean lattice $B_n$, that is, the power set of $[n]:=\{1,2,\dots,n\}$, ordered by inclusion. As an important in
Externí odkaz:
http://arxiv.org/abs/2106.02226
Autor:
Griggs, Jerrold R.
Let $L(G)$ denote the maximum number of leaves in any spanning tree of a connected graph $G$. We show the (known) result that for the $n$-cube $Q_n$, $L(Q_n) \sim 2^n = |V(Q_n)|$ as $n\rightarrow \infty$. Examining this more carefully, consider the m
Externí odkaz:
http://arxiv.org/abs/1905.13292
Publikováno v:
Order 38, 441-453 (2021)
Building on classical theorems of Sperner and Kruskal-Katona, we investigate antichains $\mathcal F$ in the Boolean lattice $B_n$ of all subsets of $[n]:=\{1,2,\dots,n\}$, where $\mathcal F$ is flat, meaning that it contains sets of at most two conse
Externí odkaz:
http://arxiv.org/abs/1704.00067
Akademický článek
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Autor:
Dove, Andrew P., Griggs, Jerrold R.
We are interested in maximizing the number of pairwise unrelated copies of a poset $P$ in the family of all subsets of $[n]$. We prove that for any $P$ the maximum number of unrelated copies of $P$ is asymptotic to a constant times the largest binomi
Externí odkaz:
http://arxiv.org/abs/1309.6686
Publikováno v:
Integers 14A (2014): #A4
We prove a "supersaturation-type" extension of both Sperner's Theorem (1928) and its generalization by Erdos (1945) to k-chains. Our result implies that a largest family whose size is x more than the size of a largest k-chain free family and that con
Externí odkaz:
http://arxiv.org/abs/1303.4336
Autor:
Griggs, Jerrold R., Li, Wei-Tian
Given a finite poset $P$, we consider the largest size $\lanp$ of a family $\F$ of subsets of $[n]:=\{1,...,n\}$ that contains no subposet $P$. This continues the study of the asymptotic growth of $\lanp$; it has been conjectured that for all $P$, $\
Externí odkaz:
http://arxiv.org/abs/1208.4241
Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of $[n]:=\{1,...,n\}$ that contains no subposet P. This problem has been studied intensively in recent years, and it is conjectured that $\pi(P):= \lim_{n\rightarrow\
Externí odkaz:
http://arxiv.org/abs/1010.5311