On Two Bijections from S_n (321) to S_n (132)

D Saracino - arXiv preprint arXiv:1008.4557, 2010 - arxiv.org
… a bijection from Sn(321) to Sn(132) in [5], by giving bijections from each set onto the set Dn of
Dyck paths of length 2n. (Knuth’s bijection from Sn(132) … bijections from Sn(321) to Sn(132) …

Classification of bijections between 321-and 132-avoiding permutations

A Claesson, S Kitaev - Discrete Mathematics & Theoretical …, 2008 - dmtcs.episciences.org
bijections as bijections from 321- to 132-avoiding permutations; we apply trivial transformations
if a bijection … a bijection between Sn(321) and Sn(231). They show that a permutation is …

On bijections for pattern-avoiding permutations

J Bloom, D Saracino - Journal of Combinatorial Theory, Series A, 2009 - Elsevier
… we show that an analogous bijection from Sn(132) onto Sn(213) does the … bijection Θ is
obtained by combining two previously known bijections: a bijection of Knuth [4] between Sn(321) …

Another look at bijections for pattern-avoiding permutations

J Bloom, D Saracino - Advances in Applied Mathematics, 2010 - Elsevier
… In this section we will describe the bijection Γ : Sn(321) → Sn(132) by describing σ and Γ (σ)
pictorially in terms of what we will call the L-corners of σ. These L-corners are defined in …

Permutations restricted by two distinct patterns of length three

A Robertson - Advances in Applied Mathematics, 2001 - Elsevier
2 we know sn α β for α β ∈ 123 132, 132 123 . Using the reversal and complementation
bijections presented in Section 2 … Trivially, we have sn 123 321 = 0 for n ≥ 6. The enumeration …

Refined restricted permutations

A Robertson, D Saracino, D Zeilberger - Annals of Combinatorics, 2002 - Springer
321-avoiding derangements are enumerated by Fine’s sequence. We will investigate two
bijections… We have that Bn is the set of 132-avoiding bijections on {1, 2,...,n}. However, in order …

Restricted permutations

R Simion, FW Schmidt - European Journal of Combinatorics, 1985 - Elsevier
Two such bijections will involve the 0-1 strings counted by the … We shall first prove all
statements for p = 321. The SYT … 213 = 132*, we only need to prove the formulae for In(132) and …

A simple and unusual bijection for Dyck paths and its consequences

S Elizalde, E Deutsch - Annals of Combinatorics, 2003 - Springer
… several applications of our bijections to enumeration of statistics in 321- and 132-avoiding …
132-avoiding permutations to Dyck paths. The first bijection, which we denote Ψ: Sn(321) −…

Restricted simsun permutations

E Deutsch, S Elizalde - Annals of Combinatorics, 2012 - Springer
… We will use a well-known bijection between 132-avoiding … n + 2 with no UDU and no DUD,
which are also counted by Sn (… occurrence πb−1πbπd of 321 such that all entries between …

Fixed points and excedances in restricted permutations

S Elizalde - the electronic journal of combinatorics, 2011 - combinatorics.org
… We will use the bijection between Sn(132) and Dn given by Krattenthaler in [10], which we
… did to define ψ, some other known bijections between Sn(321) and Dn can easily be viewed …