论文标题
在最小的演示文稿中，有很少的发电机的仿射半群
On minimal presentations of shifted affine semigroups with few generators
论文作者
论文摘要
Aggine Semigroup是$（\ Mathbb z _ {\ ge 0}^d， +）$的有限生成的子群，而数值半群是一个具有$ d = 1 $的仿射半群。越来越多的作品越来越多地研究了数值半群的家族，即形式的数值半群的家庭$ m_n = \ langle n + r_1，\ ldots，n + r_k \ rangle $ for固定$ r_1，\ r_1，\ ldots，r_k $，r_k $，r_k $，r_k $ for shift os for shift osshife os Shift $ n $ n $ n $ n $ n。已经表明，在任何变化的数值半群家族中，任何最小呈现的大小都是有限的（实际上，这种大小最终在$ n $中是周期性的）。在本文中，我们考虑转移了仿期半群的家庭，并证明了一些（但不是全部）转移的4生成仿射半群的家庭任意最小的陈述。
An affine semigroup is a finitely generated subsemigroup of $(\mathbb Z_{\ge 0}^d, +)$, and a numerical semigroup is an affine semigroup with $d = 1$. A growing body of recent work examines shifted families of numerical semigroups, that is, families of numerical semigroups of the form $M_n = \langle n + r_1, \ldots, n + r_k \rangle$ for fixed $r_1, \ldots, r_k$, with one semigroup for each value of the shift parameter $n$. It has been shown that within any shifted family of numerical semigroups, the size of any minimal presentation is bounded (in fact, this size is eventually periodic in $n$). In this paper, we consider shifted families of affine semigroups, and demonstrate that some, but not all, shifted families of 4-generated affine semigroups have arbitrarily large minimal presentations.
