Partial clones determined by concatenated relations

Let k/spl ges/2, k be a k-element set, /spl rho//sub 1/ and /spl rho//sub 2/ two relations on k and let /spl rho//sub 1//spl ominus//spl rho//sub 2/ be the concatenation of /spl rho//sub 1/ and /spl rho//sub 2/. We study the link between the partial clones pPol /spl rho//sub 1//spl cap/pPol /spl rho//sub 2/ and pPol (/spl rho//sub 1//spl ominus//spl rho//sub 2/). Using results arising from this study we address the following problem: given two maximal partial clones M/sub 1/ and M/sub 2/ over k, under what conditions is the partial clone M/sub 1//spl cap/M/sub 2/ covered by M/sub 1/ or by M/sub 1/? So far the research in this direction was focused on partial clones of Boolean functions and on Slupecki type maximal partial clones.