\documentclass{minimal}
\usepackage{luacode}
\begin{document}
\begin{luacode*}
local yhvh = { 'Y', 'H', 'V', 'H' }
for i = 1,4 do
    for j = 1,4 do
	for k = 1,4 do
	    if i ~= j and i ~= k and j ~= k then
		local l = 10 - (i + j + k)
		tex.sprint( yhvh[i], yhvh[j], yhvh[k], yhvh[l], '\\qquad' )
	    end
	end
    end
    tex.sprint('\\par')
end
\end{luacode*}
\end{document}