GENERALIZATIONS OF SCHUR PARTITION THEOREM

被引：36

作者：

ALLADI, K ^{[1
]}

GORDON, B ^{[1
]}

机构：

[1] UNIV CALIF LOS ANGELES,DEPT MATH,LOS ANGELES,CA 90024

来源：

MANUSCRIPTA MATHEMATICA | 1993年 / 79卷 / 02期

关键词：

D O I：

10.1007/BF02568332

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Schur's partition theorem states that the number of partitions of n into distinct parts = 1, 2 (mod 3) is equal to the number of partitions of n into parts with minimal difference 3 and no consecutive multiples of 3. A three-parameter generalization of Gleissberg's refinement of Schur's theorem is obtained by showing that PI(m=1)infinity (1 + aq(m))(1 + bq(m)) is equal to the numerator of a certain continued fraction. Two proofs axe presented, one completely combinatorial, and one using generating functions.

引用

页码：113 / 126

页数：14

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