Combinatorial enumeration of weighted Catalan numbers
Name
727153781-MIT.pdf
Description
Full printable version
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2.25 MB
Format
Adobe PDF
Checksum (MD5)
49ce0beaa0a30fa71fe9984473aeae99
Author(s)
An, Junkyu
Advisor(s)
Alexander Postnikov.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
This thesis is devoted to the divisibility property of weighted Catalan and Motzkin numbers and its applications. In Chapter 1, the definitions and properties of weighted Catalan and Motzkin numbers are introduced. Chapter 2 studies Wilf conjecture on the complementary Bell number, the alternating sum of the Stirling number of the second kind. Congruence properties of the complementary Bell numbers are found by weighted Motkin paths, and Wilf conjecture is partially proved. In Chapter 3, Konvalinka conjecture is proved. It is a conjecture on the largest power of two dividing weighted Catalan number, when the weight function is a polynomial. As a corollary, we provide another proof of Postnikov and Sagan of weighted Catalan numbers, and we also generalize Konvalinka conjecture for a general weight function.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 69-70).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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