Publication Date:
2013-06-19
Description:
Let B k , i ( n ) be the number of partitions of n with certain difference condition and let A k , i ( n ) be the number of partitions of n with certain congruence condition. The Rogers–Ramanujan–Gordon theorem states that B k , i ( n )= A k , i ( n ). Lovejoy obtained an overpartition analogue of the Rogers–Ramanujan–Gordon theorem for the cases i =1 and i = k . We find an overpartition analogue of the Rogers–Ramanujan–Gordon theorem in the general case. Let D k , i ( n ) be the number of overpartitions of n satisfying certain difference condition and C k , i ( n ) be the number of overpartitions of n whose non-overlined parts satisfy certain congruence condition. We show that C k , i ( n )= D k , i ( n ). By using a function introduced by Andrews, we obtain a recurrence relation that implies that the generating function of D k , i ( n ) equals the generating function of C k , i ( n ). By introducing the Gordon marking of an overpartition, we find a generating function formula for D k , i ( n ) that can be considered an overpartition analogue of an identity of Andrews for ordinary partitions.
Print ISSN:
0024-6115
Electronic ISSN:
1460-244X
Topics:
Mathematics
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