We show that if P is a lattice polytope in the nonnegative orthant of R and χ is a coloring of the lattice points in the orthant such that the color χ(a+b) depends only on the colors χ(a) and χ(b), then the number of colors of the lattice points in the dilation nP of P is for large n given by a polynomial (or, for rational P , by a quasipolynomial). This unifies a classical result of Ehrhart an...

Weakly left ample semigroups form a class of semigroups that are (2; 1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation to the identity map in the domain of. They are semigroups with commuting idempotents such that the e R-class of any element a contains a (necessarily unique) idempotent a + , e R is a left congruence, and the ample identit...