Gordon,s Partition Theorem
المؤلف:
Gordon, B.
المصدر:
"A Combinatorial Generalization of the Rogers-Ramanujan Identities." Amer. J. Math. 83
الجزء والصفحة:
...
23-8-2019
1722
Gordon's Partition Theorem
Let 
denote the number of partitions into 
parts not congruent to 0, 
, or 
(mod 
). Let 
denote the number of partitions of 
wherein
1. 1 appears as a part at most 
times.
2. The total number of appearances of 
and 
(i.e., any two consecutive integers) together is at most 
.
Then Gordon's partition theorem states that for 
,
The first Rogers-Ramanujan identity corresponds to 
, and the second to 
, 
.
REFERENCES:
Andrews, G. E. and Santos, J. P. O. "Rogers-Ramanujan Type Identities for Partitions with Attached Odd Parts." Ramanujan J. 1, 91-99, 1997.
Gordon, B. "A Combinatorial Generalization of the Rogers-Ramanujan Identities." Amer. J. Math. 83, 393-399, 1961.
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