GeorgeAndrews和DaveRobbins的q-TSPP猜想的证明（模有限量的常规计算）
A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a finite amount of routine calculations)
摘要：
在历史性的会议Combinatoire枚举[LL]精彩举办的吉尔伯特拉贝尔和皮埃尔勒鲁有许多刺激的讲座，包括一个非常有趣的皮埃尔勒鲁本人，谁谈到了他的联合工作与泽维尔Viennot[LV]，解决微分方程combinatorially！在皮埃尔·勒鲁主持的同一次座谈会的问题会议上，理查德·斯坦利提出了一些关于平面划分枚举的有趣问题，后来他将这些问题扩展成了一篇引人入胜的文章。大多数这些问题涉及枚举的对称类的平面分区，这是更详细地讨论了另一篇文章斯坦利[Sta 2]。后一篇文章中的所有命题都已被证明（见Dave Bressoud的现代经典[B]），除了一个，到目前为止，抵制了枚举组合学中最伟大的头脑的努力。它涉及到全对称平面分拆的q-计数的一个显式公式的证明，由George Andrews和Dave Robbins独立证明（[Sta 2]，[Sta 1]（conj.7），[B]（conj.13））。在向皮埃尔·勒鲁致敬的这篇文章中，我们描述了如何证明这最后的堡垒。
英文摘要：
In the historic conference Combinatoire Enumerative[LL] wonderfully organized by Gilbert Labelle and Pierre Leroux there were many stimulating lectures, including a very interesting one by Pierre Leroux himself, who talked about his joint work with Xavier Viennot[LV], on solving differential equations combinatorially! During the problem session of that very same colloque, chaired by Pierre Leroux, Richard Stanley raised some intriguing problems about the enumeration of plane partitions, that he later expanded into a fascinating article[Sta1]. Most of these problems concerned the enumeration of symmetry classes of plane partitions, that were discussed in more detail in another article of Stanley[Sta2]. All of the conjectures in the latter article have since been proved (see Dave Bressoud's modern classic[B]), except one, that, so far, resisted the efforts of the greatest minds in enumerative combinatorics. It concerns the proof of an explicit formula for the q-enumeration of totally symmetric plane partitions, conjectured independently by George Andrews and Dave Robbins([Sta2],[Sta1](conj. 7), [B](conj. 13)). In this tribute to Pierre Leroux, we describe how to prove that last stronghold.
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。
