教师姓名：法瑞德阿里尼偶法尔德
教师英文名称：Farid Aliniaeifard
教师拼音名称：FaridAliniaeifard
入职时间：2025-05-06
所在单位：高等研究院、数学与交叉科学研究中心、非线性期望前沿科学研究中心
性别：男
联系方式：Office E422,
Research Center for Mathematics and Interdisciplinary Sciences,
72 Binhai Road, Jimo District, Qingdao, Shandong Province, China Post Code：266237
主要任职：Professor of Mathematics
论文名称：F. Aliniaeifard and S. van Willigenburg, The extra basis in noncommuting variables, Adv. in Appl. Math. 168 (2025) [20 pages]
摘要：We answer a question of Bergeron, Hohlweg, Rosas, and Zabrocki from 2006 to give a combinatorial description for the coproduct of the x-basis in the Hopf algebra of symmetric functions in noncommuting variables, NCSym, which arises in the theory of Grothendieck bialgebras. We achieve this by applying the theory of Hopf monoids and the Fock functor. We also determine combinatorial expansions of this basis in terms of the monomial and power sum symmetric functions in NCSym, and by taking the commutative image of the x-basis we discover a new multiplicative basis for the algebra of symmetric functions.
https://doi.org/10.1016/j.aam.2025.102887
arXiv:2409.00177
论文类型：期刊论文
是否译文：否
