Let S be a numerical monoid with minimal generating set 〈n1, …, nt〉. For m ∈ S, if [Formula: see text], then [Formula: see text] is called a factorization length of m. We denote by ℒ(m) = {m1, …, mk} (where mi < mi+1 for each 1 ≤ i < k) the set of all possible factorization lengths of m. The Delta set of m is defined by Δ(m) = {mi+1 - mi | 1 ≤ i < k} and the Delta set of S by Δ(S) = ⋃m∈SΔ(m). In this paper, we expand on the study of Δ(S) begun in [C. Bowles, S. T. Chapman, N. Kaplan and D. Reiser, On delta sets of numerical monoids, J. Algebra Appl. 5 (2006) 1–24] in the following manner. Let r1, r2, …, rt be an increasing sequence of positive integers and Mn = 〈n, n + r1, n + r2, …, n + rt〉 a numerical monoid where n is some positive integer. We prove that there exists a positive integer N such that if n > N then |Δ(Mn)| = 1. If t = 2 and r1 and r2 are relatively prime, then we determine a value for N which is sharp.

We ask whether iconic co-speech gestures are judged as more natural by naive participants when their content is entailed by a preceding context, or repeated in the same utterance, or when they contribute new information (i.e., are nontrivial). Our results show, first, that the acceptability of co-speech gestures is not affected by whether they are entailed by a preceding context (they are not "hard presupposition triggers"). In contrast, our second finding is that gestures are affected by content in the same utterance, such that they are judged more acceptable when they reinforce information already present in the proposition. In addition, gestures varied widely in how acceptable they were judged even in the same information contexts, which we take to be an indication that we are just scratching the surface of a more general question about the felicity of co-speech gestures, of which the current study provides a first experimental foundation.