IIIT Hyderabad Publications |
|||||||||
|
Partitions and Weighted Integer CompositionsAuthor: Sumit Kumar Date: 2021-08-09 Report no: IIIT/TH/2021/91 Advisor:Girish Varma AbstractThis thesis concerns the subject of integer partitions. It has found numerous applications including in the study of black holes and in the area of statistical mechanics. A major area of investigation in its own right, it has been called “topic filled with the true romance of mathematics”. Our investigation leads to following results in the subject: • A combinatorial identity for the number of integer partitions of n in terms of certain weighted integer compositions of n. • A combinatorial identity for the sum of positive divisors of n in terms of certain weighted integer compositions of n. • A combinatorial identity for the number of representations of a positive integer n as a sum of k squares. • A combinatorial identity for the number of representations of a positive integer n as a sum of k triangular numbers. • A combinatorial identity for the number of plane partitions of a positive integer n. • Some combinatorial identities for the Bernoulli numbers in terms of Stirling numbers of the second kind. In deriving each of the above results, we highlight a useful combination of generating function techniques with the Faa di Bruno formula. Full thesis: pdf Centre for Others |
||||||||
Copyright © 2009 - IIIT Hyderabad. All Rights Reserved. |