Arctic Curves Phenomena for Bounded Lecture Hall Tableaux
Arctic Curves Phenomena for Bounded Lecture Hall Tableaux
复制标题
有界演讲厅画面的北极曲线现象
DOI：
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发表时间：
2019
影响因子：
2.4
通讯作者：
Matthew Nicoletti
中科院分区：
文献类型：
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作者：
S. Corteel;D. Keating;Matthew Nicoletti
最近，第一作者和Jang Soo Kim在他们的多元小q-Jacobi多项式的研究中引入了讲堂场景。然后，他们列举了有界的报告厅场景，并表明他们的列举与标准和半标准的杨氏场景密切相关。本文利用另外两种组合模型研究了这些有界表的渐近行为：面为正方形和五边形的图上的不相交路径和面为六边形和八边形的格上的二聚体模型。本文用切线法研究了不相交点阵路径模型中的北极曲线，该点阵路径具有固定的起点和终点，并按任意分段可微函数分布。然后，我们研究了二聚体模型，并使用ansatz猜测了Kasteleyn逆的渐近性，这证实了两个例子中用切线法计算的北极曲线。
Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related to standard and semistandard Young tableaux. In this paper we study the asymptotic behavior of these bounded tableaux thanks to two other combinatorial models: non-intersecting paths on a graph whose faces are squares and pentagons and dimer models on a lattice whose faces are hexagons and octagons. We use the tangent method to investigate the arctic curve in the model of non-intersecting lattice paths with fixed starting points and ending points distributed according to some arbitrary piecewise differentiable function. We then study the dimer model and use an ansatz to guess the asymptotics of the inverse of the Kasteleyn, which confirm the arctic curve computed with the tangent method for two examples.
通过切线法绘制有缺陷的阿兹特克矩形的北极曲线
影响因子：
1.6
作者：
Di Francesco, Philippe;Guitter, Emmanuel
通讯作者：
Guitter, Emmanuel
DOI：
10.1088/1751-8121/aad028
发表时间：
2018
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
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作者：
Di Francesco, Philippe;Guitter, Emmanuel
通讯作者：
Guitter, Emmanuel