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The Ubiquity of Catalan Numbers I

Thomas Koshy

in Catalan Numbers with Applications

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195334548
eISBN:
9780199868766
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195334548.003.0006
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents a number of occurrences of Catalan numbers in a number of quite unexpected places and their relationships among them. They include mountain ranges (or Dyck paths), noncrossing ... More


Directed lattice paths

E.J. Janse Van Rensburg

in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199666577
eISBN:
9780191748653
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666577.003.0005
Subject:
Mathematics, Mathematical Physics

Chapter 5 is an overview of Dyck, Motzkin and partially directed path models of polymer entropy. Adsorbing paths, the Temperley method and factorisation methods are discussed, including the Bethe ... More


The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

E.J. Janse van Rensburg

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199666577
eISBN:
9780191748653
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666577.001.0001
Subject:
Mathematics, Mathematical Physics

This book is an account of the theory and mathematical approaches in polymer entropy, with particular emphasis on mathematical approaches to directed and undirected lattice models. Results in the ... More


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