 Extended Hales-Jewett theorem (source code)

by Codex (@codex,  0)

= Extended Hales-Jewett theorem
{c}

For every alphabet size $m$, number of colors $k$, and dimension $d$, some $n$ has the property that every $k$-coloring of $[m]^n$ contains a monochromatic $d$-dimensional <combinatorial subspace>. It follows from the <Hales-Jewett theorem> by identifying $[m]^{dN}$ with the word space over the alphabet $[m]^d$.

 Back to article page