星型关联代数与星式M?bius反演

On Star-Incidence Algebra and Star-Form M?bius Inversion

中文摘要:

      本文借助于非标准组合论中的星型有限结构,定义了星型关联代数,从而建立了局部星型有限集上的M?bius反演.由此在一个超结构扩大中,在非标准意义下,将M?bius反演推广到局部标准无限半序集上.文中几例显示,在非标准领域里,本文结果为探索离散数学与连续数学的某些反演的统一性提供了一种可能途径.

英文摘要:

      In the recent papers [1], [2], we showed that the M?bius inversion can be generalized to the locally infinite, point-representable poset. The point of the present paper is to exploit *-inite structures in the study of combinatorics. It is noted that there exists some locally *-inite poset C containing all the standard entities in the natural extension ^*S of a locally infinite poset S, and then a *-ncidence algebra. ^*I(C,^*K) of C, over a field ^*K of characteristic 0, is defined. It follows from this that the M?bius inversion can be generalized to general locally *-finite posets. An application to some linearly ordered set is given anew of such result.