報 告 人：Volkmar Welker 教授

報告題目：Partial orders on decompositions of combinatorial structures 

報告時間：2024年09月23日（周一）下午4：00

報告地點：分測中心102會議室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

       Volkmar Welker，德國馬爾堡大學教授。主要從事代數組合、離散幾何、組合交換代數等領域的研究。研究成果多次發表在Mem. Amer. Math. Soc.，Adv. Math.，Math. Z.，Trans. Amer. Math. Soc.，J. Algebra等高水平期刊上。

報告摘要：

       For a combinatorial object which has a subobject poset we present conditions under which one can define meaningful posets or partial or full decompositions of the object and ordered analogs thereof. A classical example for such an object is a finite set and its subset poset which then leads to the posets of partial or full set partitions andtheir ordered analogs, all ordered by refinement. Similarly, one can start with a finite dimensional vectorspace over a finite field, its poset of subspaces and consider posets of partial or full direct sum decompositions of the vectorspace ordered by refinement.We show that there are many other structures for which these constructions make sense.In all cases we ask for enumerative invariants, such as the M\obius number of the posets, and consider geometric invariants (e.g., homotopy type) defined through theorder complex of the posets. The talk will contain many examples, some with complete solutions and some with challenging questions.