On a question of Douglass and Ono

Florian Luca (Stellenbosch University)

12-Nov-2024, 13:00-14:00 (5 months ago)

Abstract: It is known that the partition function p(n)p(n) obeys Benford's law in any integer base b2b\ge 2. A similar result was obtained by Douglass and Ono for the plane partition function PL(n)\text{PL}(n) in a recent paper. In their paper, Douglass and Ono asked for an explicit version of this result. In particular, given an integer base b2b\ge 2 and string ff of digits in base bb they asked for an explicit value N(b,f)N(b,f) such that there exists nN(b,f)n\le N(b,f) with the property that PL(n)\text{PL}(n) starts with the string ff when written in base bb. In my talk, I will present an explicit value for N(b,f)N(b,f) both for the partition function p(n)p(n) as well as for the plane partition function PL(n)\text{PL}(n).

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )


One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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Organizers: Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner*
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