Landman, Bruce M.

3-accessibility of Fibonacci numbers ★★

Author(s): Landman; Robertson

\begin{question} Is the set of Fibonacci numbers 3-accessible? \end{question}

Keywords: Fibonacci numbers; monochromatic diffsequences

2-accessibility of primes ★★

Author(s): Landman; Robertson

\begin{question} Is the set of prime numbers 2-accessible? \end{conjecture}

Keywords: monochromatic diffsequences; primes

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.

\begin{conjecture} For all $k$ and $\ell$ with $k \geq \ell$, $w(k,\ell) \geq w(k+1,\ell-1)$. \end{conjecture}

Keywords: arithmetic progression; van der Waerden

The large sets conjecture ★★★

Author(s): Brown; Graham; Landman

\begin{conjecture} If $A$ is 2-large, then $A$ is large. \end{conjecture}

Keywords: 2-large sets; large sets

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