Refined Cauchy and Littlewood identities, plane partitions and symmetry classes of alternating sign matrices
Refined Cauchy and Littlewood identities, plane partitions and symmetry classes of alternating sign matrices
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改进的柯西和利特伍德恒等式、平面划分和交替符号矩阵的对称类
DOI：
10.1016/j.jcta.2015.08.007
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
M. Wheeler
中科院分区：
文献类型：
--
作者：
D. Betea;M. Wheeler
本文证明并猜想了一些新的对称函数恒等式，它们等价于1.平面剖分在一定的限制和加权条件下和2.交替符号矩阵在一定的对称性条件下的生成列.我们的每一个恒等式的左手边是一个相关柯西或利特尔伍德恒等式的简单精化，允许它们被解释为平面划分的生成级数。每个恒等式的右边是六顶点模型在相关域上的配分函数。这些可以被解释为交替符号矩阵生成系列，使用众所周知的双射与六顶点模型配置。
We prove and conjecture some new symmetric function identities, which equate the generating series of1.Plane partitions, subject to certain restrictions and weightings, and2.Alternating sign matrices, subject to certain symmetry properties. The left hand side of each of our identities is a simple refinement of a relevant Cauchy or Littlewood identity, allowing them to be interpreted as generating series for plane partitions. The right hand side of each identity is a partition function of the six-vertex model, on a relevant domain. These can be interpreted as generating series for alternating sign matrices, using the well known bijection with six-vertex model configurations.