论文标题
在某些数值半群中的frobenius数量上
On the Frobenius number of certain numerical semigroups
论文作者
论文摘要
令$ 0<λ\ leq1 $，$λ\ notin \ weft \ {\ frac24，\ frac27，\ frac2 {10}，\ frac2 {13}，\ ldots \ right \ right \} $，be a a prime和$ p $ a prime a prime a prime a prime a prime a prime $ [p，p+λp]，用$f_λ（p）$表示最大的整数，无法将其写入$ [p，p+λp] $的总和。然后\ [f_λ（p）\ sim \ left \ lfloor2+\frac2λ\ right \ rfloor \ rfloor \ cdot p \ text {，as} p \ text {to infinity {to infinity} \] \] 此外，关于“改变货币的问题”的WILF的问题对所有$ P $的分数都有积极的答案，其中包含来自$ [P，2p] $的素数。特别是，这适用于所有素数不少于$ p $产生的半群。后一个特殊情况已经在上一篇论文中显示。
Let $0<λ\leq1$, $λ\notin\left\{\frac24, \frac27, \frac2{10}, \frac2{13}, \ldots\right\}$, be a real and $p$ a prime number, with $[p,p+λp]$ containing at least two primes. Denote by $f_λ(p)$ the largest integer which cannot be written as a sum of primes from $[p,p+λp]$. Then \[f_λ(p)\sim\left\lfloor2+\frac2λ\right\rfloor\cdot p\text{, as }p\text{ goes to infinity.}\] Further a question of Wilf about the 'Money-Changing Problem' has a positive answer for all semigroups of multiplicity $p$ containing the primes from $[p,2p]$. In particular, this holds for the semigroup generated by all primes not less than $p$. The latter special case was already shown in a previous paper.
