Abstract
Abstract Let λ be a partition of the positive integer n chosen uniformly at random among all such partitions. Let Ln = L n (λ) and M n = M n (λ) be the largest part size and its multiplicity, respectively. For large n, we focus on a comparison between the partition statistics L n and L n M n . In terms of convergence in distribution, we show that they behave in the same way. However, it turns out that the expectation of L n M n – L n grows as fast as 1 2 log n {1 \over 2}\log n . We obtain a precise asymptotic expansion for this expectation and conclude with an open problem arising from this study.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
