Top to random shuffles and characterization of rigged configurations of B(infinity) in type A

1 Top to Random Shuffling
	1.1 Introduction
	1.2 Preliminaries
	1.3 Multiplication Formula for Arbitrary Finite Products
		1.3.1 A Bijection between Shuffles and Set Partitions
		1.3.2 Explicit Formula for the Coefficients |Qja|
		1.3.3 Applications
	1.4 Generalizations to the Algebra of G-Permutations
		1.4.1 G-permutations and Shuffling Cards with Multiple Faces
		1.4.2 Top to Random Shuffling Expansion Formula in Q[SnG]
		1.4.3 Other Generalizations
	1.5 Further Discussions
2 Marginally Large Tableaux and Rigged Configurations
	2.1 Introduction
	2.2 Marginally Large Tableaux and Cascading Sequences
		2.2.1 Marginally Large Tableaux
		2.2.2 Cascading Sequences and a Bijection
		2.2.3 Lanes of Cascading Sequences
	2.3 Cascading Sequences and Rigged Configurations
		2.3.1 Rigged Configurations
		2.3.2 Kashiwara Operators Acting in a Cascading Sequence Arrangement
		2.3.3 Obtaining the Rigged Configuration from the Cascading Sequence Using Lanes
		2.3.4 Notations and Rough Idea of the Algorithm
		2.3.5 Plateaus as Base for Construction
		2.3.6 Adding Boxes to a Stretch
		2.3.7 Unrefined Procedure Generating All Rigged Configurations
		2.3.8 Proof of the Procedures for Adding Boxes
		2.3.9 Determining the Cascading Sequence of a Rigged Configuration
		2.3.10 Growth Algorithm
	2.4 Further Discussions