The 1/3-2/3 Conjecture for N-Free Ordered Sets
The 1/3-2/3 Conjecture for N-Free Ordered Sets
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N-自由有序集的 1/3-2/3 猜想
DOI：
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发表时间：
2011
影响因子：
0.7
通讯作者：
I. Zaguia
中科院分区：
文献类型：
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作者：
I. Zaguia
有序集合$P=(V,\leq)$中的平衡对是$V$的元素对$(x,y)$，使得$P$的线性扩展中把$x$放在$y$之前的比例在实区间$[1/3, 2/3]$内。证明了每一个不完全有序的有限$N$自由有序集都有一个平衡对。
A balanced pair in an ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of linear extensions of $P$ that put $x$ before $y$ is in the real interval $[1/3, 2/3]$. We prove that every finite $N$-free ordered set which is not totally ordered has a balanced pair.