1 Abstract. Let S = {si}i∈IN ⊆ IN be a numerical semigroup. For si ∈ S, let ν(si) denote the number of pairs (si−sj , sj) ∈ S . When S is the Weierstrass semigroup of a family {Ci}i∈IN of one-point algebraicgeometric codes, a good bound for the minimum distance of the code Ci is the Feng and Rao order bound dORD(Ci) := min{ν(sj) : j ≥ i+ 1}. It is well-known that there exists an integer m such ...

for the E-valued unknown function u, where E is a Banach space, B is the generator of a (linear) C0-semigroup on E, ut is the history function defined by ut(s) = u(t + s) and Φ is the delay operator. We will employ the semigroup approach on L-phase space (in the spirit of [4] and [5]) to be able to apply numerical splitting schemes to this problem. We prove convergence of theses schemes, invest...

Notation 1.1. Let X be a projective variety over an algebraically closed field. For every integer k ≥ 0, denote by Nk(X) the finitely-generated free Abelian group of k-cycles modulo numerical equivalence, and denote by N(X) the k graded piece of the quotient algebra A∗(X)/Num∗(X), cf. [Ful98, Example 19.3.9]. For every Z-module B, denote Nk(X)B := Nk(X)⊗B, resp. N(X)B := N(X)⊗B. Denote by NEk(X...

We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semi...

A numerical semigroup $S$ is cyclotomic if its polynomial $P_S$ a product of polynomials. The number irreducible factors (with multiplicity) the length $\ell(S)$ $S.$ We show that complete intersection $\ell(S)\le 2$. This establishes particular case conjecture Ciolan, Garc\'{i}a-S\'{a}nchez and Moree (2016) claiming every intersection. In addition, we investigate relation between embedding dim...

For given positive integers a1,a2,⋯,ak with gcd(a1,a2,⋯,ak)=1, the denumerant d(n)=d(n;a1,a2,⋯,ak) is number of nonnegative solutions (x1,x2,⋯,xk) linear equation a1x1+a2x2+⋯+akxk=n for a integer n. p, let Sp=Sp(a1,a2,⋯,ak) be set all n’s such that d(n)>p. In this paper, by introducing p-numerical semigroup, where N0\Sp finite, we give explicit formulas p-Frobenius number, which maximum N0\S...

Let A be an alphabet with two elements. Considering a particular class of words (the phrases) over such an alphabet, we connect with the theory of numerical semigroups. We study the properties of the family of numerical semigroups which arise from this starting point.

Given a numerical semigroup S = 〈a1, a2, . . . , aν〉 in canonical form, let M(S) := S \ {0}. Define associated numerical semigroups B(S) := {x ∈ N0 : x + M(S) ⊆ M(S)} and L(S) := 〈a1, a2 − a1, . . . , aν − a1〉 . Set B0(S) = S, and for i ≥ 1, define Bi(S) := B(Bi−1(S)). Similarly, set L0(S) = S, and for i ≥ 1, define Li(S) := L(Li−1(S)). These constructions define finite ascending chains of semi...