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Properties of Some Markov Chains on Linear Extensions of Posets

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Author(s): Kara Stasikelis
Series: PhD thesis at Clemson University
Edition: version 23 Nov 2018
Year: 2018

Language: English
Commentary: Downloaded from https://tigerprints.clemson.edu/all_dissertations/2104?utm_source=tigerprints.clemson.edu%2Fall_dissertations%2F2104&utm_medium=PDF&utm_campaign=PDFCoverPages
Pages: 116

Recommended Citation......Page 1
Title Page......Page 2
Abstract......Page 3
Acknowledgments......Page 4
List of Tables......Page 7
List of Figures......Page 8
Introduction......Page 9
Tsetlin library......Page 14
Hyperplane arrangements......Page 16
Pop shuffles......Page 21
Bands......Page 28
Extended promotion operator......Page 33
Self-organizing libraries......Page 42
Properties of the Promotion Markov Chain on Linear Extensions......Page 47
The case of one ladder......Page 52
Proof of Theorem 3.0.1......Page 60
Partition function and convergence rates......Page 69
Self-Organizing Libraries with a Poset Structure on the Leaves......Page 76
Background on R-trivial monoids......Page 79
When the leaf posets are rooted forests......Page 82
Background on the class DO(Ab)......Page 91
When the leaf posets are unions of an ordinal sum of a forest and a ladder: an algebraic treatment......Page 95
When the leaf posets are unions of an ordinal sum of a forest and a ladder: a combinatorial treatment......Page 100
Future Directions and Discussion......Page 107
Bibliography......Page 114