ewt -- Effective weight of a semigroup (Pflueger)

The effective weight of a semigroup S is defined as the number of pairs (a,b) such that a is a minimal generator of S and b is a gap of S with a<b.

By contrast, the weight of S (the sum of the ramification indices of the corresponding Weierstrass point) may be defined as the number of pairs (a,b) such that a is in S and b is a gap with a<b.

Improving on work of Eisenbud-Harris (who proved that primitive semigroups S are Weierstrass), and occur in codimension equal to the weight of S), Nathan Pflueger introduced the "effective weight" and showed that all semigroups with genus g and effective weight w<g are Weierstrass, and occur on a subvariety of M_(g,1) with codimension w.

For example, semigroups generated by two elements are always Weierstrass since complete intersections are smoothable; they are almost never primitive,

Pflueger, Nathan . On nonprimitive Weierstrass points. Algebra Number Theory 12 (2018), no. 8, 1923–1947.