منابع مشابه
Crossing and Alignments of Permutations
We derive the continued fraction form of the generating function of some new q-analogs of the Eulerian numbers Êk,n(q) introduced by Lauren Williams building on work of Alexander Postnikov. They are related to the number of alignments and weak exceedances of permutations. We show how these numbers are related to crossing and generalized patterns of permutations We generalize to the case of deco...
متن کاملCrossings and Nestings for Arc-Coloured Permutations
The equidistribution of many crossing and nesting statistics exists in several combinatorial objects like matchings, set partitions, permutations, and embedded labelled graphs. The involutions switching nesting and crossing numbers for set partitions given by Krattenthaler, also by Chen, Deng, Du, Stanley, and Yan, and for permutations given by Burrill, Mishna, and Post involved passing through...
متن کاملOn the complexity of crossings in permutations
We investigate crossing minimization problems for a set of permutations, where a crossing expresses a disarrangement between elements. The goal is a common permutation π∗ which minimizes the number of crossings. In voting and social science theory this is known as the Kemeny optimal aggregation problem minimizing the Kendall-τ distance. This rank aggregation problem can be phrased as a one-side...
متن کاملOn k-crossings and k-nestings of permutations
We introduce k-crossings and k-nestings of permutations. We show that the crossing number and the nesting number of permutations have a symmetric joint distribution. As a corollary, the number of k-noncrossing permutations is equal to the number of k-nonnesting permutations. We also provide some enumerative results for k-noncrossing permutations for some values of k. Résumé. Nous introduisons l...
متن کاملCrossings and Nestings for Arc-Coloured Permutations and Automation
Symmetric joint distribution between crossings and nestings was established in several combinatorial objects. Recently, Marberg extended Chen and Guo’s result on coloured matchings to coloured set partitions following a multi-dimensional generalization of the bijection and enumerative methods from Chen, Deng, Du, Stanley, and Yan. We complete the study for arc-coloured permutations by establish...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2007
ISSN: 0196-8858
DOI: 10.1016/j.aam.2006.01.006