The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the q-bracket, is a quasimodular form. More generally, if a graded algebra A of functions on partitions has the property that the q-bracket of every element is a quasimodular form of the same weight, we call A a quasimodular algebra. We introduce a new quasimodular algebra \(\mathcal {T}\) consisting of symmetric polynomials in the part sizes and multiplicities.

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对称的Bloch–Okounkov定理

分区上的所谓移位对称函数的代数具有以下性质：对于所有元素，称为q括号的某个生成级数 是准模数形式。更一般而言，如果分区上的函数的渐变代数 A具有每个元素的 q括号是同等权重的拟模形式的性质，则我们将 A称为拟模代数。我们引入了一个新的准模块化代数\（\ mathcal {T} \），该代数 由零件大小和多重性的对称多项式组成。