Other publication
Singmaster’s conjecture in the interior of Pascal’s triangle
Authors: Matomäki Kaisa
Conference name: Russian-Finnish Symposium on Discrete Mathematics
Publisher: Turku Centre for Computer Science
Publishing place: Turku
Publication year: 2021
Book title : Proceedings of the Sixth Russian-Finnish Symposium on Discrete Mathematics
Series title: TUCS Lecture Notes
Number in series: 31
First page : 23
Last page: 23
ISBN: 978-952-12-4113-0
ISSN: 1797-8831
Web address : http://urn.fi/URN:ISBN:978-952-12-4113-0
In 1971, David Singmaster conjectured that any natural number greater than one only appears in Pascal’s triangle a bounded number of times. In the talk I will discuss what is known about this conjecture, concentrating on a recent result in joint work with Maksym Radziwill, Xuancheng Shao, Terence Tao, and Joni Ter¨av¨ainen that establishes the conjecture in the interior region of the triangle. While the problem is combinatorial, we use number theoretic and analytic tools. In particular an important analytic input in our proof is Vinogradov’s estimate for exponential sums over primes
