一类数字半群容许的型

Admissible Patterns on a Class of Numerical Semigroups

本文探究一类特殊的数字半群所容许的齐次线性型,证明这一类数字半群容许任意的强容许型、减法度大于等于2的减法型以及可容许度大于等于2的布尔型。同时还探究了被这一类数字半群及其极大理想所容许的非齐次线性型,即这一类数字半群的极大理想容许长度为n,常数项为PFn(S,M(S))的型。

It is studied the admissible patterns on a special class of numerical semigroups. This paper explores the admissible homogeneous linear patterns on this class of numerical semigroups, and proves that this class of numerical semigroups admits arbitrary strongly admissible patterns, subtraction pattern with a degree greater than or equal to 2 and Boolean pattern with admissibility degree greater than or equal to 2. At the same time, this paper also explores the admissible non-homogeneous linear patterns on this class of numerical semigroups and its maximal ideal, that is, the maximal ideal allowable length of this class of numerical semigroups is n and the constant term is PFn( S,M( S)).