拟完整解与限制格点游动
The Quasi-Holonomic Ansatz and Restricted Lattice Walks
摘要：
伟大的计数器学家热尔曼·克雷韦拉斯（Germain Kreweras）凭经验发现了这一有趣的事实，然后需要大量的篇幅和人类的聪明才智来证明这一点。其他伟大的计数器学家，例如海因里希·尼德豪森（Heinrich Niederhausen）、艾拉·杰塞尔（Ira Gessel）和米雷耶·布斯克-梅卢（Mireille Bousquet-Mélou），找到了其他巧妙的、“更简单”的证明。但没有一个像我们这样简单！我们的证明（在我们忠实的计算机的慷慨帮助下）在传统意义上是“丑陋的”，因为对于一个卑微的人来说，遵循所有的步骤是痛苦的。但根据我们卑微的审美品味，这个证明要优雅得多，因为它（概念上）是单行的。因此，如果这条线相当长（一个由一般计数函数满足的巨大的部分递归方程），它占用的存储空间比一张分辨率很低的照片少。
英文摘要：
The great enumerator Germain Kreweras empirically discovered this intriguing fact, and then needed lots of pages[K], and lots of human ingenuity, to prove it. Other great enumerators, for example, Heinrich Niederhausen[N], Ira Gessel[G1], and Mireille Bousquet-Mélou[B], found other ingenious, ``simpler'' proofs. Yet none of them is as simple as ours! Our proof (with the generous help of our faithful computers) is ``ugly'' in the traditional sense, since it would be painful for a lowly human to follow all the steps. But according to our humble aesthetic taste, this proof is much more elegant, since it is (conceptually) one-line. So what if that line is rather long (a huge partial-recurrence equation satisfied by the general counting function), it occupies less storage than a very low-resolution photograph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
