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
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.
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页码:113 / 126
页数:14
相关论文
共 13 条
[1]  
ALLADI K, IN PRESS J COMB TH A
[2]  
ALLADI K, IN PRESS GENERALIZAT
[3]  
ANDREWS GE, 1991, J REINE ANGEW MATH, V413, P198
[4]  
ANDREWS GE, 1976, ENCY MATH, V0002
[5]  
ANDREWS GE, 1969, AM J MATH, V191, P18
[6]  
ANDREWS GE, 1968, ACTA ARITH, V4, P429
[7]  
ANDREWS GE, 1967, GLASGOW MATH J, V9, P127
[8]   A COMBINATORIAL PROOF OF A REFINEMENT OF THE ANDREWS-OLSSON PARTITION IDENTITY [J].
BESSENRODT, C .
EUROPEAN JOURNAL OF COMBINATORICS, 1991, 12 (04) :271-276
[9]  
BRESSOUD DM, 1979, J REINE ANGEW MATH, V305, P215
[10]   A COMBINATORIAL PROOF OF SCHUR 1926 PARTITION THEOREM [J].
BRESSOUD, DM .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 79 (02) :338-340