Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster, who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle other than the number 1, which is the only number that appears infinitely many times. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThere is a finite upper bound on the multiplicities of entries in Pascal's triangle, other than the number 1, which appears infinitely many times. 1 Proposed Year Progress Toward ResolutionOpen. Singmaster showed in 1971 that the number of occurrences N(a) of a value a is O(log a); Abbott, Erdos and Hanson (1974) improved this to O(log a / log log a), and Kane (2007) gave the best known unconditional bound. The number 3003 appears eight times and is the only number known to do so; it is not known whether any number appears more than eight times. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Singmaster's Conjecture (Wikipedia)
Sources
1. Singmaster's Conjecture (Wikipedia)
Wikimedia FoundationLead section
named after the British mathematician David Singmaster who proposed it in 1971
Lead section, statement sentence
there is a finite upper bound on the multiplicities of entries in Pascal's triangle
Open questions section
It is not known whether any number appears more than eight times, nor whether any number besides 3003 appears that many times.
Known bound section, 1974 refinement
(1974) (see References) refined the estimate to
In Branch: Number Theory, Lead sentence
ter's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who propos
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.