Let S be a numerical semigroup with embedding dimension e(S), Frobenius number g(S), and type t(S). Put n(S) := Card(S ∩ {0, 1, . . . , g(S)}). A question of Wilf is shown to be equivalent to the statement that e(S)n(S) ≥ g(S)+1. This question is answered affirmatively if S is symmetric, pseudo-symmetric, or of maximal embedding dimension. The question is also answered affirmatively in the foll...

Embeddings are diffeomorphisms between some unseen physical attractor and a reconstructed image. Different embeddings may or may not be equivalent under isotopy. We regard embeddings as representations of the attractor, review the labels required to distinguish inequivalent representations for an important class of dynamical systems, and discuss the systematic ways inequivalent embeddings becom...