A generalization of the Simion-Schmidt bijection for restricted permutations

Stackable and queueable permutations

There is a natural bijection between permutations obtainable using a stack (those avoiding the pattern 312) and permutations obtainable using a queue (those avoiding 321). This bijection is equivalent to one described by Simion and Schmidt in 1985. We argue that this bijection might well have been found back in 1968 by readers of volume 1 of Knuth's *The Art of Computer Programming*, if Knuth had not assigned difficulty ratings to his exercises.

Bijective Approaches for Schmidt-Type Theorems

We provide new Schmidt-type results through an investigation of two bijections, which are results involving partitions with parts counted only at given indices. Mork's bijection, the first of these, was originally given as a proof of Schmidt's theorem. We show that a version of Sylvester's bijection is equivalent to Mork's bijection applied to 2-modular diagrams, which implies refinements of existing results and new generating function identities. We then develop a bijection based on an idea appearing in a recent paper of Andrews and Keith, that places partitions counted at the indices $r$, $t…

Classification of bijections between 321- and 132-avoiding permutations

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 …

Restricted simsun permutations

A permutation is simsun if for all k, the subword of the one-line notation consisting of the k smallest entries does not have three consecutive decreasing elements. Simsun permutations were introduced by Simion and Sundaram, who showed that they are counted by the Euler numbers. In this paper we enumerate simsun permutations avoiding a pattern or a set of patterns of length 3. The results involve Motkzin, Fibonacci, and secondary structure numbers. The techniques in the proofs include generating functions, bijections into lattice paths and generating trees.

促进与行运动在有理Catalan组合学中

Promotion and rowmotion in rational Catalan combinatorics

本文研究了促进与行运动在有理Catalan组合学中的等价性，通过扩展双射与RSK类对应关系，揭示了 generalized Dyck paths 上的双射性质。

按逆序数计数的模式避免排列

Pattern Avoiding Permutations Enumerated by Inversions

该论文以逆序数为计数参数，研究长度不超过3的排列模式组合的避免计数，并聚焦于不可分解排列，扩展了Simion和Schmidt的经典方法。