Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Constant Term Identities
Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions and Constant Term Identities
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发表时间：
2007
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通讯作者：
M. Ishikawa
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作者：
M. Ishikawa
本文给出了“Self-complementary totally symmetric plane partitions”（J. Combin.理论系列A 42，277-292）由米尔斯，罗宾斯和拉姆西。本文还解决了猜想6的一个弱版本，即，在特定对合下不变的移位平面划分的数目等于在垂直翻转下不变的交替符号矩阵的数目。
In this paper we give Pfaan or determinant expressions, and constant term iden- tities for the conjectures in the paper "Self-complementary totally symmetric plane partitions" (J. Combin. Theory Ser. A 42, 277-292) by Mills, Robbins and Rumsey. We also settle a weak version of Conjecture 6 in the paper, i.e., the number of shifted plane partitions invariant under a certain involution is equal to the number of alternating sign matrices invariant under the vertical flip.