论文标题
$ k $的类似物，标记为强烈单峰序列的杜尔菲符号
An analogue of $k$-marked Durfee symbols for strongly unimodal sequences
论文作者
论文摘要
在2007年开创性的论文中，安德鲁斯引入了一类组合对象，这些对象概括了称为$ k $标记的durfee符号。许多对象的多变量等级生成函数已显示出在统一根的某些向量上具有有趣的模块化属性。由于最近对强烈单峰序列的等级生成函数的研究激励，我们采用了安德鲁斯的方法来定义一种类似的组合对象，称为$ k $，具有强烈的单峰符号，该符号强烈地概括了强烈的单峰序列。我们为这些对象建立了多元等级生成函数，我们在组合上研究了这些对象。我们通过讨论该等级生成函数的潜在量子模块化属性在Unity根部的某些向量上。
In a seminal 2007 paper, Andrews introduced a class of combinatorial objects that generalize partitions called $k$-marked Durfee symbols. Multivariate rank generating functions for these objects have been shown by many to have interesting modularity properties at certain vectors of roots of unity. Motivated by recent studies of rank generating functions for strongly unimodal sequences, we apply methods of Andrews to define an analogous class of combinatorial objects called $k$-marked strongly unimodal symbols that generalize strongly unimodal sequences. We establish a multivariate rank generating function for these objects, which we study combinatorially. We conclude by discussing potential quantum modularity properties for this rank generating function at certain vectors of roots of unity.
