Counting Permutations that Avoid Many Patterns

Counting Permutations that Avoid Many Patterns
By
Yonah BIERS-ARIEL, Haripriya CHAKRABORTY, John CHIARELLI, Bryan EK, Andrew LOHR, Jinyoung PARK, Justin SEMONSEN, Richard VOEPEL, Mingjia YANG, Anthony ZALESKI, and Doron ZEILBERGER
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Written: Dec, 2016-Feb. 28; Posted March 7, 2017. This version: March 8, 2017.
Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org .

This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are many patterns to be avoided. The choices of projects contained herein were made collectively by Dr. Z.'s Fall 2016 Experimental Mathematics.

Added March 8, 2017: It turns out that Toufik Mansour (see also wikipedia page), that, among many other things, is one of the greatest experts in the world on permutation patterns, along with his collaborators, has already explored the many facets of avoiding many patterns, in a very systematic way. So many of the discoveries reported in the latter sections of the present article has been already published by them. See the many references in Toufik Mansour's Email message that he kindly allowed us to post here.

Maple packages

VATTER.txt, a Maple package written by Doron Zeilberger that accompanied this paper, it is need for the new package below.

VATTERPLUS.txt, a Maple package new to this project. Must have VATTER.txt in the same directory.

HCRV.txt, a Maple package for guessing polynomials
YBE.txt, Maple code supporting Section 2

SmallExp.txt, Another Maple package for guessing polynomials and other things.

Sample Input and Output Files

For systematic study of Wilf classes that are ultimately counted by polynomials, see the following output file,

For enumeration schemes for sets of patterns one of length 4, and one of length 5 see the following output file v45.txt,

For enumeration schemes for sets of patterns one of length 4, and two of length 5 see the following output file v455.txt,

For enumeration schemes for sets of patterns three of length 4, and one of length 5 see the following output file v4445.txt,

For enumeration schemes for sets of patterns two of length 4, and two of length 5 see the following output file v4455.txt,

For enumeration schemes for sets of patterns one of length 4, and three of length 5 see the following output file v4555.txt,

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
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