A (v, b, r, k) combinatorial configuration is a (r, k)-biregular bipartite graph with v vertices on the left and b vertices on the right and with no cycle of length 4. Combinatorial configurations have become very important for some cryptographic applications to sensor networks and to peerto-peer communities. Configurable tuples are those tuples (v, b, r, k) for which a (v, b, r, k) combinatori...

A curveX is said to be of type (N, γ) if it is anN–sheeted covering of a curve of genus γ with at least one totally ramified point. A numerical semigroup H is said to be of type (N, γ) if it has γ positive multiples of N in [N, 2Nγ] such that its γ element is 2Nγ and (2γ + 1)N ∈ H. If the genus of X is large enough and N is prime, X is of type (N, γ) if and only if there is a point P ∈ X such t...

The Goto number of a parameter ideal Q in a Noetherian local ring (R, m) is the largest integer q such that Q : m is integral over Q. The Goto numbers of the monomial parameter ideals of R = k[[x1 , x2 , . . . , xν ]] are characterized using the semigroup of R. This helps in computing them for classes of numerical semigroup rings, as well as on a case by case basis. The minimal Goto number of R...

A numerical semigroup is a sub-semigroup of the natural numbers that has finite complement. Some key properties are its Frobenius number [Formula: see text], genus text] and type text]. It known for any Numerical semigroups with called almost symmetric, we introduce new property characterizes them. We give an explicit characterization show fixed eventually constant large The also

Three conjectures #1999–8, #1999–9 and #1999–10 which were posed by V. Arnold [2] and devoted to the statistics of the numerical semigroups are refuted for the case of semigroups generated by three positive integers d 1 , d 2 , d 3 with gcd(d 1 , d 2 , d 3) = 1. Weak asymptotics of conductor C(d 1 , d 2 , d 3) of numerical semigroup and fraction p(d 1 , d 2 , d 3) of a segment [0; C(d 1 , d 2 ,...