Complete intersections in certain affine and projective monomial curves

Let k be an arbitrary field, the purpose of this work is to provide families of positive integers A = {d(1), ..., d(n)} such that either the toric ideal I-A of the affine monomial curve C = {(t(d1),..., t(dn)) vertical bar t is an element of k}subset of A(k)(n) or the toric ideal I-A star of its projective closure C-star subset of P-k(n) is a complete intersection. More precisely, we characterize the complete intersection property for I-A and for I-A star when: (a) A is a generalized arithmetic sequence, (b) A \ {d(n)} is a generalized arithmetic sequence and d(n) is an element of Z(+), (c) A consists of certain terms of the (p, q)-Fibonacci sequence, and (d) A consists of certain terms of the (p, q)-Lucas sequence. The results in this paper arise as consequences of those in [3, 5] and some new results regarding the toric ideal of the curve.