Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure after Shuffles (Part 2)

Preprint

16 April 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0104003

Abstract

Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like: cut a deck into roughly two equal piles, thoroughly mix the first pile and then riffle it with the second pile. Conclusions are drawn concerning the distribution of fixed points and the asymptotic distribution of cycle structure. An upper bound on the convergence rate is given. Connections are made with extended Schur functions and with work of Baik and Rains.

Keywords

BERELE/REMMEL/KEROV/VERSHIK VARIATION
INCREASING SUBSEQUENCE STRUCTURE
SYMMETRIC FUNCTIONS
CONVERGENCE RATE
SHUFFLING
RAINS
PILE

All Related Versions

Version 1, 2001-03-31, ArXiv
Version 2, 2001-04-16, ArXiv

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