Home » Author index

Landman, Bruce M.


Combinatorics

3-accessibility of Fibonacci numbers ★★

Author(s): Landman; Robertson

Question   Is the set of Fibonacci numbers 3-accessible?

Keywords: Fibonacci numbers; monochromatic diffsequences

Posted by vjungic
updated August 24th, 2008
add new comment
Combinatorics

2-accessibility of primes ★★

Author(s): Landman; Robertson

Question   Is the set of prime numbers 2-accessible?

Keywords: monochromatic diffsequences; primes

Posted by vjungic
updated July 9th, 2008
add new comment
Combinatorics » Ramsey Theory

Concavity of van der Waerden numbers ★★

Author(s): Landman

For $ k $ and $ \ell $ positive integers, the (mixed) van der Waerden number $ w(k,\ell) $ is the least positive integer $ n $ such that every (red-blue)-coloring of $ [1,n] $ admits either a $ k $-term red arithmetic progression or an $ \ell $-term blue arithmetic progression.

Conjecture   For all $ k $ and $ \ell $ with $ k \geq \ell $, $ w(k,\ell) \geq w(k+1,\ell-1) $.

Keywords: arithmetic progression; van der Waerden

Posted by Bruce Landman
updated June 21st, 2007
add new comment
Combinatorics » Ramsey Theory

The large sets conjecture ★★★

Author(s): Brown; Graham; Landman

Conjecture   If $ A $ is 2-large, then $ A $ is large.

Keywords: 2-large sets; large sets

Posted by vjungic
updated June 10th, 2007
add new comment
Syndicate content