论文标题
Gessel数量交替卷积的因素
Factors of Alternating Convolution of the Gessel Numbers
论文作者
论文摘要
The Gessel number $P(n,r)$ is the number of the paths in plane with $(1, 0)$ and $(0,1)$ steps from $(0,0)$ to $(n+r, n+r-1)$ that never touch any of the points from the set $\{(x,x)\in \mathbb{Z}^2: x\geq r\}$.我们表明，Gessel数字$ P（N，R）$与超级加泰罗尼亚数字$ S（N，R）$之间存在密切的关系。通过使用新总和，我们证明了Gessel数字$ p（n，r）$的交替卷积总是可以由\ frac {1} {2} {2} $ s（n，r）$除外。
The Gessel number $P(n,r)$ is the number of the paths in plane with $(1, 0)$ and $(0,1)$ steps from $(0,0)$ to $(n+r, n+r-1)$ that never touch any of the points from the set $\{(x,x)\in \mathbb{Z}^2: x\geq r\}$. We show that there is a close relationship between the Gessel numbers $P(n,r)$ and the super Catalan numbers $S(n,r)$. By using new sums, we prove that an alternating convolution of the Gessel numbers $P(n,r)$ is always divisible by \frac{1}{2}$S(n,r)$.
