2023, Vol. 4, Issue 1, Part B
A study on partition theory
Author(s): Bijendra Kumar and Rajeev Ranjan Jha
Abstract: Partition theory, a branch of number theory, explores the different ways an integer can be expressed as the sum of positive integers, known as partitions. This field has deep historical roots, with significant contributions from mathematicians like Leonhard Euler and Srinivasa Ramanujan. The partition function P(n), which counts the number of distinct partitions of an integer n, lies at the heart of the theory. Generating functions, Ferrers diagrams, and Young tableaux are key tools used to analyze partitions. Important results in the field include the Rogers-Ramanujan identities and the Hardy-Ramanujan asymptotic formula, both of which have profound implications in combinatorics, representation theory, and mathematical physics. Partition theory's modern relevance extends to advanced areas such as modular forms, q-series, and statistical mechanics. Despite its longstanding history, partition theory continues to be an active research area, with ongoing exploration of its connections to other mathematical disciplines and the discovery of new partition identities and formulas.
Pages: 156-159 | Views: 205 | Downloads: 136
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How to cite this article:
Bijendra Kumar and Rajeev Ranjan Jha. A study on partition theory. Journal of Mathematical Problems, Equations and Statistics. 2023; 4(1): 156-159.