### Abstract

We also give a recursive description of the algorithmic bijection given by Richards in 1988 (combined with a bijection by Knuth from 1969). This bijection is equivalent to the celebrated bijection of Simion and Schmidt (1985), as well as to the bijection given by Krattenthaler in 2001, and it respects 11 statistics - the largest number of statistics any of the bijections respects.

Language | English |
---|---|

Article number | B60d |

Number of pages | 30 |

Journal | Séminaire Lotharingien de Combinatoire |

Volume | 60 |

Publication status | Published - 4 Nov 2008 |

### Fingerprint

### Keywords

- bijection
- permutation statistics
- equidistribution
- pattern avoidance
- Catalan structures

### Cite this

*Séminaire Lotharingien de Combinatoire*,

*60*, [B60d].

}

*Séminaire Lotharingien de Combinatoire*, vol. 60, B60d.

**Classification of bijections between 321- and 132-avoiding permutations.** / Claesson, Anders; Kitaev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Classification of bijections between 321- and 132-avoiding permutations

AU - Claesson, Anders

AU - Kitaev, Sergey

PY - 2008/11/4

Y1 - 2008/11/4

N2 - It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs of this fact. It turns out that some of the published bijections can easily be obtained from others. In this paper we describe all bijections we were able to find in the literature and show how they are related to each other via "trivial" bijections. We classify the bijections according to statistics preserved (from a fixed, but large, set of statistics), obtaining substantial extensions of known results. Thus, we give a comprehensive survey and a systematic analysis of these bijections.We also give a recursive description of the algorithmic bijection given by Richards in 1988 (combined with a bijection by Knuth from 1969). This bijection is equivalent to the celebrated bijection of Simion and Schmidt (1985), as well as to the bijection given by Krattenthaler in 2001, and it respects 11 statistics - the largest number of statistics any of the bijections respects.

AB - It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs of this fact. It turns out that some of the published bijections can easily be obtained from others. In this paper we describe all bijections we were able to find in the literature and show how they are related to each other via "trivial" bijections. We classify the bijections according to statistics preserved (from a fixed, but large, set of statistics), obtaining substantial extensions of known results. Thus, we give a comprehensive survey and a systematic analysis of these bijections.We also give a recursive description of the algorithmic bijection given by Richards in 1988 (combined with a bijection by Knuth from 1969). This bijection is equivalent to the celebrated bijection of Simion and Schmidt (1985), as well as to the bijection given by Krattenthaler in 2001, and it respects 11 statistics - the largest number of statistics any of the bijections respects.

KW - bijection

KW - permutation statistics

KW - equidistribution

KW - pattern avoidance

KW - Catalan structures

UR - http://www.emis.de/journals/SLC/index.html

M3 - Article

VL - 60

JO - Séminaire Lotharingien de Combinatoire

T2 - Séminaire Lotharingien de Combinatoire

JF - Séminaire Lotharingien de Combinatoire

SN - 1286-4889

M1 - B60d

ER -