Pattern-avoiding permutations and Brownian excursion, part II: fixed points

Christopher Hoffman; Douglas Rizzolo; Erik Slivken

doi:10.1007/s00440-016-0732-2

Pattern-avoiding permutations and Brownian excursion, part II: fixed points

Probability Theory and Related Fields ◽

10.1007/s00440-016-0732-2 ◽

2016 ◽

Vol 169 (1-2) ◽

pp. 377-424 ◽

Cited By ~ 5

Author(s):

Christopher Hoffman ◽

Douglas Rizzolo ◽

Erik Slivken

Keyword(s):

Fixed Points ◽

Brownian Excursion ◽

Pattern Avoiding Permutations

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Pattern-avoiding permutations and Brownian excursion part I: Shapes and fluctuations

Random Structures and Algorithms ◽

10.1002/rsa.20677 ◽

2016 ◽

Vol 50 (3) ◽

pp. 394-419 ◽

Cited By ~ 5

Author(s):

Christopher Hoffman ◽

Douglas Rizzolo ◽

Erik Slivken

Keyword(s):

Brownian Excursion ◽

Pattern Avoiding Permutations

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Multiple Pattern Avoidance with respect to Fixed Points and Excedances

The Electronic Journal of Combinatorics ◽

10.37236/1804 ◽

2004 ◽

Vol 11 (1) ◽

Cited By ~ 7

Author(s):

Sergi Elizalde

Keyword(s):

Fixed Points ◽

Generating Functions ◽

Pattern Avoidance ◽

Arbitrary Length ◽

Dyck Paths ◽

Main Technique ◽

Single Pattern ◽

Pattern Avoiding Permutations

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 subset of patterns of length 3. The main technique is to use bijections between pattern-avoiding permutations and certain kinds of Dyck paths, in such a way that the statistics in permutations that we study correspond to statistics on Dyck paths that are easy to enumerate.

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