# Algorithms for permutation statistics

@inproceedings{Zeilberger2011AlgorithmsFP, title={Algorithms for permutation statistics}, author={Doron Zeilberger and Andrew M. Baxter}, year={2011} }

Two sequences u; v of n positive integers are order isomorphic if their terms are in the same relative order. A permutation p said to contain permutation q as a pattern if there is some subsequence of p which is order isomorphic to q. This subsequence is called a copy of q. This notion of pattern containment is generalized to include adjacency restrictions as per dashed patterns. The primary permutation statistics studied in this work are written in terms of the number of copies of a given…

## 6 Citations

### Refining Enumeration Schemes to Count According to Permutation Statistics

- Mathematics, Computer ScienceElectron. J. Comb.
- 2014

It is proved that when a finite enumeration scheme exists to compute the number of permutations avoiding a given set of vincular patterns, the scheme can also compute the distribution of certain permutation statistics with very little extra computation.

### Subregularity in infinitely labeled generating trees of restricted permutations

- Mathematics, Computer ScienceAdv. Appl. Math.
- 2022

### Some Wilf-equivalences for vincular patterns

- Mathematics
- 2015

We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating…

### Noncommutative Bell polynomials and the dual immaculate basis

- Mathematics
- 2017

We define a new family of noncommutative Bell polynomials in the algebra of free quasi-symmetric functions and relate it to the dual immaculate basis of quasi-symmetric functions. We obtain…

### Automatic Generation of Theorems and Proofs on Enumerating Consecutive-Wilf Classes

- Mathematics
- 2013

This article, describes two complementary approaches to enumeration, the positive and the negative, each with its advantages and disadvantages. Both approaches are amenable to automation, and we…

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