有序分拆与无序分拆的分拆恒等式与计数公式  

Partition Identity and Counting Formulae between Partitions and Compositions

作　　者：庞荣波[1] 

机构地区：[1]聊城大学东昌学院,山东聊城252000

出　　处：《四川师范大学学报（自然科学版）》2010年第3期312-316,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10871116);山东省自然科学基金(Y2006A04)资助项目

摘　　要：自从欧拉对正整数的分拆进行正式研究后,现在该问题已成为组合数学、图论、数论研究的一个重要课题.近年来,一些国内外数学研究者对研究有序分拆与无序分拆提出了新的思路和方法.在研究正整数的无序分拆与有序分拆相关问题的基础上,利用Agarwal的组合法和Frobenius-分拆,获得了一些无序分拆与有序分拆之间的恒等式,并给出了一些有序分拆的分拆数计算公式,此结论进一步丰富和发展了正整数分拆理论.After Leonhard Euler studied formally the partition of positive integer,this problem has already become an important topic in the research of the combinatorial mathematics,graph theory,number theory.Recently,some mathematical researchers at home and abroad put forward new ideas and methods about partitions and compositions,on the basis of related problems between partitions and compositions of positive integers,by using Agarwal＇s combinatorial method and Frobenius-partition studying some identities between partitions and compositions and counting formulae of the compositions are given.The conclusion enriched and promoted the partition of positive intege.

关 键 词：无序分拆 有序分拆 分拆恒等式 

分 类 号：O157.1[理学—数学]