On restricted permutations on regular multisets
On restricted permutations on regular multisets
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发表时间：
2013-06
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通讯作者：
Marie-Louise Bruner
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作者：
Marie-Louise Bruner
模式避免从普通排列扩展到多集上的排列产生了几个有趣的计数结果。我们研究正则多集上的排列，即每个元素出现相同次数的多集。对于这种情况，我们填补了Heubach和Mansour(2006)工作中的一个空白，并完成了避免一对长度为3的模式的排列的研究。在所研究的所有情况下，都给出了闭合计数公式，并出现了众所周知的序列。我们把Stanley-Wilf猜想推广到多集和词上的置换，作为本文的结束语。
The extension of pattern avoidance from ordinary permutations to those on multisets gave birth to several interesting enumerative results. We study permutations on regular multisets, i.e., multisets in which each element occurs the same number of times. For this case, we close a gap in the work of Heubach and Mansour (2006) and complete the study of permutations avoiding a pair of patterns of length three. In all studied cases, closed enumeration formulae are given and well-known sequences appear. We conclude this paper by some remarks on a generalization of the Stanley-Wilf conjecture to permutations on multisets and words.