On the commutative equivalence of semi-linear sets of Nk N k
Given two subsets S1,S2 S 1 , S 2 of Nk N k , we say that S1 S 1 is commutatively equivalent to S2 S 2 if there exists a bijection f:S1?S2 f : S 1 ? S 2 from S1 S 1 onto S2 S 2 such that, for every v?S1 v ? S 1 , |v|=|f(v)| | v | = | f ( v ) | , where |v| | v | denotes the sum of the components of v. We prove that every semi-linear set of Nk N k is commutatively equivalent to a recognizable subset of Nk N k .
commutative equivalence semilinear set recognizable set