Weighted Inversion Numbers, Restricted Growth Functions, and Standard Young Tableaux
Weighted Inversion Numbers, Restricted Growth Functions, and Standard Young Tableaux
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加权反转数、限制增长函数和标准 Young Tableaux
DOI：
10.1016/0097-3165(85)90044-5
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
Kevin W. J. Kadell
中科院分区：
文献类型：
--
作者：
Kevin W. J. Kadell
我们给出了一族具有相同母函数的加权反演数，它们插值于反演数和MacMahon主指数之间。Foata的双射是从一个简单的对合中自然地得到的。另一种证明使用q-差分方程，产生一些新的结果。我们得到了一个新的生成函数的限制增长函数和两个q-类似的公式的数量的标准扬tableaux的给定形状。虽然第一个真的可以追溯到麦克马洪，第二个使用我们的加权反转数之一，似乎是新的。
We give a family of weighted inversion numbers with the same generating function which interpolate between the inversion number and MacMahon's major index. Foata's bijection is obtained in a natural way from a simple involution. An alternative proof usesq-difference equations which yield some new results. We obtain a new generating function for restricted growth functions and twoq-analogs of a formula for the number of standard Young tableaux of a given shape. While the first really goes back to MacMahon, the second uses one of our weighted inversion numbers and appears to be new.