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Abstract: We study the distribution of the statistics `number of fixed points' and `number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving generating functions enumerating these two statistics. Some cases are generalized to patterns of arbitrary length. For avoidance of one single pattern we give partial results. We also describe the distribution of these statistics in involutions avoiding any... (Update)
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2.7: Multiple Pattern Avoidance with Respect to Fixed Points and.. - Elizalde (2004) (Correct)
0.8: Pattern Avoidance in Permutations: Linear and Cyclic Orders - Vella (2003) (Correct)
0.6: On the Wilf-Stanley limit of 4231-avoiding.. - Albert, Elder.. (2005) (Correct)
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0.3: Bijections for Refined Restricted Permutations - Elizalde, Pak (2004) (Correct)
0.2: Permutation Statistics of Indexed and Poset Permutations - Steingrímsson (Correct)
0.1: Dumont's Statistic on Words - Skandera (2000) (Correct)
BibTeX entry: (Update)
@misc{ elizalde-multiple,
author = "Sergi Elizalde",
title = "Multiple Pattern Avoidance with Respect to Fixed Points and Excedances",
url = "citeseer.ist.psu.edu/article/elizalde04multiple.html" }
Citations (may not include all citations):267 Enumerative Combinatorics (context) - Stanley - 1997
108 An Introduction to the Analysis of Algorithms (context) - Sedgewick, Flajolet - 1996
61 Combinatorial aspects of continued fractions (context) - Flajolet - 1980
60 Some Combinatorial Properties of Schubert Polynomials - Billey, Jockusch et al. - 1993
53 Restricted Permutations (context) - Simion, Schmidt - 1985
35 Generating trees and the Catalan and Schroder numbers (context) - West - 1995
26 Permutations with restricted patterns and Dyck paths - Krattenthaler - 2001
26 Generating Trees and Forbidden Subsequences - West - 1996
12 Dyck path enumeration (context) - Deutsch - 1999
9 the diagram of 132-avoiding permutations (context) - Reifegerste - 2003
7 Fixed points and excedances in restricted permutations (context) - Elizalde
4 Enumeration of permutations containing a prescribed number o.. (context) - Fulmek - 2003
2 A simple and unusual bijection for Dyck paths and its conseq.. (context) - Elizalde, Deutsch - 2003
2 Bijections for refined restricted permutations - Elizalde, Pak - 2004
2 Seminaire Lotharingien de Combinatoire (context) - Guibert, Mansour et al. - 2002
2 Refined Restricted Permutations (context) - Robertson, Saracino et al. - 2003
2 personal communication (context) - Bona, Guibert
2 Longest increasing subsequences in pattern-restricted permut.. - Deutsch, Hildebrand et al.
2 Pattern avoidance in cyclically ordered structures (context) - Vella - 2003
1 Refined Restricted Permutations Avoiding Subsets of Patterns.. (context) - Mansour, Robertson - 2003
1 Refined Restricted Involutions (context) - Deutsch, Robertson et al.
http://algo.inria.fr/flajolet/Publications/books.html)
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