| 研究実績の概要 |
In a joint work with Jan-Willem van Ittersum I finished a project on functions on partitions and their connection to q-analogues of multiple zeta values. In this project we introduce the space of polynomial functions on partitions, which is a subspace of all functions on partitions. This space can be equipped with three different products, which can be seen as natural generalizations of the harmonic and shuffle products of multiple zeta values. We show that, after applying the so-called q-bracket, that polynomial functions on partitions give rise to q-analogues of multiple zeta values. Further we show that the limits of q->1 give (generalization) of multiple zeta values. As an application we show, that other well-known families of functions on partitions, such as shifted-symmetric functions, are contained in our space. This gives relations among multiple zeta values and provides a possible bridge between enumerative geometry and the theorey of multiple zeta values.
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