Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes
Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes
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DOI：
10.1016/j.aam.2005.12.006
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发表时间：
2005-10
期刊：
影响因子：
--
通讯作者：
C. Krattenthaler
中科院分区：
文献类型：
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作者：
C. Krattenthaler
我们将Chen、Deng、Du、Stanley和Yan最近的研究结果放在匹配的交叉和嵌套上，并在ferers形状填充枚举的更大背景下设置分区，其中对其增加和减少链施加限制。当Chen等人使用类似robinson - schensted的插入/删除算法时，我们使用Fomin的增长图构建来获得我们的结果。我们将Chen等人的结果（在填充语言中是关于0-1填充的结果）扩展到任意填充。最后，我们指出，这些结果很可能是更大图景的一部分，其中还包括Jonsson关于堆栈多项式的0-1填充的最新结果，Backelin， West和Xin的结果，以及bousquet - m<s:1>和Steingrímsson关于限制模式的排列和对合的枚举的结果。特别是，我们表明，我们的生长图的双反实际上确实提供了Backelin， West和Xin以及bousquet - m<s:1>和Steingrímsson的结果的替代证明。
We put recent results by Chen, Deng, Du, Stanley and Yan on crossings and nestings of matchings and set partitions in the larger context of the enumeration of fillings of Ferrers shape on which one imposes restrictions on their increasing and decreasing chains. While Chen et al. work with Robinson–Schensted-like insertion/deletion algorithms, we use the growth diagram construction of Fomin to obtain our results. We extend the results by Chen et al., which, in the language of fillings, are results about 0-1-fillings, to arbitrary fillings. Finally, we point out that, very likely, these results are part of a bigger picture which also includes recent results of Jonsson on 0-1-fillings of stack polyominoes, and of results of Backelin, West and Xin and of Bousquet-Mélou and Steingrímsson on the enumeration of permutations and involutions with restricted patterns. In particular, we show that our growth diagram bijections do in fact provide alternative proofs of the results by Backelin, West and Xin and by Bousquet-Mélou and Steingrímsson.