# Experimental methods in permutation patterns and bijective proof

@inproceedings{Shar2016ExperimentalMI, title={Experimental methods in permutation patterns and bijective proof}, author={Nathaniel Shar}, year={2016} }

OF THE DISSERTATION Experimental Methods in Permutation Patterns and Bijective Proof by Nathaniel Shar Dissertation Director: Doron Zeilberger Experimental mathematics is the technique of developing conjectures and proving theorems through the use of experimentation; that is, exploring finitely many cases and detecting patterns that can then be rigorously proved. This thesis applies the techniques of experimental mathematics to several problems. First, we generalize the translation method of…

## References

SHOWING 1-10 OF 60 REFERENCES

### Posets of Matrices and Permutations with Forbidden Subsequences

- Mathematics
- 2003

Abstract. The enumeration of permutations with specific forbidden subsequences has applications in areas ranging from algebraic geometry to the study of sorting algorithms. We consider a ranked poset…

### PROBLEMS AND CONJECTURES PRESENTED AT THE FIFTH INTERNATIONAL CONFERENCE ON PERMUTATION PATTERNS (UNIVERSITY OF ST ANDREWS, JUNE 11–15, 2007)

- Mathematics
- 2008

We say a permutation π contains or involves the permutation σ if deleting some of the entries of π gives a permutation that is order isomorphic to σ, and we write σ ¤ π. For example, 534162 contains…

### Enumeration schemes for words avoiding permutations

- Computer Science, Mathematics
- 2010

This paper further extends the method of enumeration schemes to words avoiding permutation patterns, first introduced for permutations by Zeilberger and extended by Vatter, to the case of enumerating pattern-restricted words.

### Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps

- MathematicsJ. Comb. Theory, Ser. A
- 1997

Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem, we obtain the generating functionH(x) of all 1342-avoiding permutations of lengthnas well as…

### Catalan Numbers

- Mathematics
- 2002

Sequences and arrays whose terms enumerate combinatorial structures have many applications in computer science. Knowledge (or estimation) of such integer-valued functions is, for example, needed in…

### A Translation Method for Finding Combinatorial Bijections

- Mathematics
- 2009

Consider a combinatorial identity that can be proved by induction. In this paper, we describe a general method for translating the inductive proof into a recursive bijection. Furthermore, we will…

### Method for constructing bijections for classical partition identities.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1981

It appears that the construction of a bijection between the partitions of n with parts congruent to 1 or 4 (mod 5) and the partitions with parts differing by at least 2 and an algorithm for constructing bijections for other identities of Rogers-Ramanujan type such as the Gordon identities is found.

### The Generating Functions Enumerating 12..d-Avoiding Words with r occurrences of each of 1,2, ... , n are D-finite for all d and all r

- Mathematics
- 2014

In this article, dedicated with admiration and gratitude to guru Neil Sloane on his 75-th birthday, we observe that the generating functions for multi-set permutations that do not contain an…

### Ordered partitions avoiding a permutation pattern of length 3

- MathematicsEur. J. Comb.
- 2014