Rota-Baxter algebras and left weak composition quasi-symmetric functions
Rota-Baxter algebras and left weak composition quasi-symmetric functions
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Rota-Baxter 代数和左弱组合拟对称函数
DOI：
10.1007/s11139-016-9822-0
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发表时间：
2017
影响因子：
0.7
通讯作者：
Zhao Jianqiang
中科院分区：
文献类型：
--
作者：
Yu Houyi;Guo Li;Zhao Jianqiang
受Rota问题的启发，本文研究了Rota-Baxter代数与代数相关函数之间的关系.出发点是这样一个事实，即拟对称函数的空间是由单项拟对称函数，其索引的组合物的跨度。当复合被左弱复合（LWC）所代替时，我们得到了LWC单项拟对称函数的概念以及由此得到的LWC拟对称函数空间。与Rota的问题相一致，后者被证明同构于一个生成元上的自由交换非酉Rota-Baxter代数。将拟对称函数的P-分拆组合解释推广到左弱复合情形，得到了LWC基本拟对称函数的概念.得到了LWC单项式和LWC基本拟对称函数的变换公式，推广了拟对称函数的相应结果。本文推广了拟对称函数与多重zeta值的密切关系，研究了加权多重zeta值和多重zeta值的q模拟，并建立了一个合成公式。
Motivated by a question of Rota, this paper studies the relationship between Rota–Baxter algebras and symmetric-related functions. The starting point is the fact that the space of quasi-symmetric functions is spanned by monomial quasi-symmetric functions which are indexed by compositions. When composition is replaced by left weak composition (LWC), we obtain the concept of LWC monomial quasi-symmetric functions and the resulting space of LWC quasi-symmetric functions. In line with the question of Rota, the latter is shown to be isomorphic to the free commutative nonunitary Rota–Baxter algebra on one generator. The combinatorial interpretation of quasi-symmetric functions by P-partitions from compositions is extended to the context of left weak compositions, leading to the concept of LWC fundamental quasisymmetric functions. The transformation formulas for LWC monomial and LWC fundamental quasi-symmetric functions are obtained, generalizing the corresponding results for quasi-symmetric functions. Extending the close relationship between.quasi-symmetric functions and multiple zeta values, weighted multiple zeta values, and a q-analog of multiple zeta values are investigated, and a ecomposition formula is established.