论文标题
带有3个发电机的数值半群的graver基础
Graver bases of shifted numerical semigroups with 3 generators
论文作者
论文摘要
数值半群$ m $是在添加下关闭的非阴性整数的子集。 M $中的$ n \的分解是$ n $作为$ m $的发电机的总和，而$ m $的GRAVER基础是$ gr（m_t）$ m $之间的$ gr（m_t）$交易，从而可以在因子之间有效移动。给定积极的整数$ r_1，\ ldots，r_k $，考虑$ m_t = \ langle t + r_1，\ ldots，t + r_k \ r_k \ rangle $ $ t + rangle $ $ r_1，\ ldots，\ ldots，r_k $ a in in infeger $ teeger $在本文中，我们表征了$ gr（m_t）$ $ m_t $的$ m_t $，以$ k = 3 $在$ gr（m_t）$的形式中，$ gr（m_t）的形式是$ t $的递归结构。由于我们的结果，$ gr（m_t）$中的交易数量最终是$ t $的函数。我们还获得了准线性行为开始时获得的急剧下限。
A numerical semigroup $M$ is a subset of the non-negative integers that is closed under addition. A factorization of $n \in M$ is an expression of $n$ as a sum of generators of $M$, and the Graver basis of $M$ is a collection $Gr(M_t)$ of trades between the generators of $M$ that allows for efficient movement between factorizations. Given positive integers $r_1, \ldots, r_k$, consider the family $M_t = \langle t + r_1, \ldots, t + r_k\rangle$ of "shifted" numerical semigroups whose generators are obtained by translating $r_1, \ldots, r_k$ by an integer parameter $t$. In this paper, we characterize the Graver basis $Gr(M_t)$ of $M_t$ for sufficiently large $t$ in the case $k = 3$, in the form of a recursive construction of $Gr(M_t)$ from that of smaller values of $t$. As a consequence of our result, the number of trades in $Gr(M_t)$, when viewed as a function of $t$, is eventually quasilinear. We also obtain a sharp lower bound on the start of quasilinear behavior.
