论文标题
带有给定缺陷编号的定向理性链接的数量
The number of oriented rational links with a given deficiency number
论文作者
论文摘要
令$ u_n $为带有交叉数字$ n $的非面向和理性的链接，Ernst和Sumners在1987年获得了$ | u_n | $的精确公式。在本文中，我们研究了定向理性链接的枚举问题。令$λ_n$为带有交叉数字$ n $的定向理性链接，让$λ_n（d）$是一组带有交叉数字$ n $（$ n \ ge 2 $）和缺陷$ d $的定向理性链接。在本文中，我们为$ |λ_n| $和$ |λ_n（d）| $得出精确的公式，对于任何给定的$ n $和$ d $ \ frac {d} {2} \ rfloor）} _ {\ lfloor \ frac {n} {n} {2} \ rfloor- \ lfloor \ lfloor \ frac {d+1} {2} {2} {2} {2} {2} \ rfloor}，$ f_n^{dem $ f_n^{des $
Let $U_n$ be the set of un-oriented and rational links with crossing number $n$, a precise formula for $|U_n|$ was obtained by Ernst and Sumners in 1987. In this paper, we study the enumeration problem of oriented rational links. Let $Λ_n$ be the set of oriented rational links with crossing number $n$ and let $Λ_n(d)$ be the set of oriented rational links with crossing number $n$ ($n\ge 2$) and deficiency $d$. In this paper, we derive precise formulas for $|Λ_n|$ and $|Λ_n(d)|$ for any given $n$ and $d$ and show that $$ Λ_n(d)=F_{n-d-1}^{(d)}+\frac{1+(-1)^{nd}}{2}F^{(\lfloor \frac{d}{2}\rfloor)}_{\lfloor \frac{n}{2}\rfloor -\lfloor \frac{d+1}{2}\rfloor}, $$ where $F_n^{(d)}$ is the convolved Fibonacci sequence.
