Article
Licensed
Unlicensed
Requires Authentication
On Computation of Exact van der Waerden Numbers
-
Tanbir Ahmed
Published/Copyright:
May 31, 2012
Abstract.
The van der Waerden number
is the smallest integer m such that
in every partition 
of the set 
there is always a block 
that contains an arithmetic progression of length 
. In this paper,
we report the exact value of the previously unknown van der Waerden number 
, some lower
bounds of 
and polynomial upper-bound conjectures for 
and . We also present an efficient SAT-encoding of the number 
for 
using which we have computed the exact value of 
and some lower bounds of 
.
Received: 2011-01-30
Revised: 2011-09-14
Accepted: 2011-11-23
Published Online: 2012-05-31
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
