Ever since the introduction of the quark model to explain the confusion of high energy particles, currently in terms of six quark flavours, one question continues to persist. Why has a single free quark never been observed? This we will call the problem of quark state confinement. Not to be cofused with spatial or colour confinement. In this talk the mathematical structure corresponding to an arbitrary recoupling of particles is deduced. Importantly this includes non--associative recoupling which is fundamental in order to construct a Bose-Fermi recoupling over such groups as SU(n) whenever n>2. Mathematically the recoupling structure itself is of interest suggesting generalisations of Hopf algebras and quantum groups. Furthermore, for Bose-Fermi recouplings (that is those recouplings that lead to the Pauli exclusion principle) we deduce a quark state confinement principle. For SU(3) colour or SU(6) flavour this leads unavoidably to state confinement of quarks to mesons, baryons and their aggregates.