论文标题
数值半群和威尔夫的猜想的不变的界限
Bounds for invariants of numerical semigroups and Wilf's Conjecture
论文作者
论文摘要
给定副阳性整数$ g_1 <\ ldots <g_e $，frobenius编号$ f = f（g_1，\ ldots，g_e）$是最大的整数，不可以$ g_1，\ ldots，g_e $的线性组合表示，g_e $，g_e $，具有非模糊的integer integer系数。令$ n $表示所有代表性的非负整数的数量少于$ f $；威尔夫猜想$ f+1 \ le e n $。我们为$ g_1 $以及数值半群的类型提供界限\ rceil $和$ f+1 \ le e n^2 $。最后，如果数字半群$ s = \ langle g_1，\ ldots，g_e \ rangle $几乎是对称的，我们给出了Wilf猜想的替代性，更简单的证明。
Given coprime positive integers $g_1 < \ldots < g_e$, the Frobenius number $F=F(g_1,\ldots,g_e)$ is the largest integer not representable as a linear combination of $g_1,\ldots,g_e$ with non-negative integer coefficients. Let $n$ denote the number of all representable non-negative integers less than $F$; Wilf conjectured that $F+1 \le e n$. We provide bounds for $g_1$ and for the type of the numerical semigroup $S=\langle g_1,\ldots,g_e \rangle$ in function of $e$ and $n$, and use these bounds to prove that $F+1 \le q e n$, where $q= \left \lceil \frac{F+1}{g_1} \right \rceil$, and $F+1 \le e n^2$. Finally, we give an alternative, simpler proof for the Wilf conjecture if the numerical semigroup $S=\langle g_1,\ldots,g_e \rangle$ is almost-symmetric.
