Record number :
1531428
Title of article :
Partitions weighted by the parity of the crank
Author/Authors :
Choi، نويسنده , , Dohoon and Kang، نويسنده , , Soon-Yi and Lovejoy، نويسنده , , Jeremy، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
Pages :
13
From page :
1034
To page :
1046
Abstract :
The ‘crank’ is a partition statistic which originally arose to give combinatorial interpretations for Ramanujanʹs famous partition congruences. In this paper, we establish an asymptotic formula and a family of Ramanujan type congruences satisfied by the number of partitions of n with even crank M e ( n ) minus the number of partitions of n with odd crank M o ( n ) . We also discuss the combinatorial implications of q-series identities involving M e ( n ) − M o ( n ) . Finally, we determine the exact values of M e ( n ) − M o ( n ) in the case of partitions into distinct parts. These values are at most two, and zero for infinitely many n.
Keywords :
Congruences , partitions , Crank
Journal title :
Journal of Combinatorial Theory Series A
Journal title :
Journal of Combinatorial Theory Series A
Serial Year :
2009
Link To Document :
بازگشت