Permutations
Permutations
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DOI：
10.3840/07000127
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发表时间：
2018-10
影响因子：
0.9
通讯作者：
Richard P. Stanley
中科院分区：
文献类型：
--
作者：
Richard P. Stanley
。在过去的十年里，fl对避免排列的模式进行了大量的研究，但很少涉及到它们的穷尽世代。许多应用要求穷尽地生成服从各种约束或施加特定生成顺序的排列。本文给出了几类模式避免置换的生成算法和组合格雷码。在考虑中的家庭中，有按加泰罗尼亚、大舒罗德、佩尔、偶数指数斐波纳奇数和中心二项式Coeffi指数计算的家庭。因此，我们为{1，…，n}的所有排列的集合提供格雷码，避免了对所有ττ∈S 3的模式，并且我们得到的格雷码具有距离4或5。
. The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoiding permutations. Among the families under consideration are those counted by Catalan, large Schr¨oder, Pell, even-index Fibonacci numbers and the central binomial coefficients. We thus provide Gray codes for the set of all permutations of { 1 ,...,n } avoiding the pattern τ for all τ ∈ S 3 and the Gray codes we obtain have distances 4 or 5.