Findings from published research, checked in the open

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1,720 claims from 1,059 papers are on the record. 46 have been checked so far; the other 1,674 have no check with a result yet.

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Topic: Advanced Combinatorial Mathematics ×Clear all

2 claims from 2 papers

1. Mathematics › Advanced Combinatorial Mathematics

   Computer solution to the 17-point Erdős-Szekeres problem

   Szekeres and Peters · The ANZIAM Journal · 2006

   The authors describe a computer proof that any 17 points in the plane, no three collinear, contain a convex 6-subset, using a combinatorial model of point configurations.

   Supported1 claim, checked
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   1. Supported · 71%Any 17 points in a plane, with no three in a line, always include six that form a convex hexagon, shown here by computer proof.“We describe a computer proof of the 17-point version of a conjecture originally made by Klein-Szekeres in 1932 (now commonly known as the “Happy End Problem”) that a planar configuration of 17 points, no 3 points collinear, always contains a convex 6-subset.”

2. Mathematics › Advanced Combinatorial Mathematics

   Large cycles in generalized Johnson graphs

   Kozhevnikov and Zhukovskii · arXiv (Cornell University) · 2022

   The paper counts cycles of unbounded length in generalized Johnson graphs and obtains asymptotics for their number for certain growth rates of the cycle length.

   Unchecked1 claim
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   1. UncheckedThe paper obtains asymptotic formulas for the number of cycles in generalized Johnson graphs when the cycle length grows at certain rates.“Asymptotics of the number of such cycles is obtained for certain growth rates of the cycle length.”