DATE:
Tuesday, September 6 (2011), at 1:55pm
PLACE: LIT 368
SPEAKER:
Ali Bulent Ekin (Ankara, Turkey)
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TITLE:
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Some missing inequalities for the rank and the crank of partitions and
certain products in the 11-dissection of the partition function
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ABSTRACT:
Let N(r; m; n) ( resp. M(r; m; n) ) denote the number of partitions of n with rank (resp. crank )
congruent to r mod m. In this talk we prove some inequalities among N(r; m; n) when m = 5 and 7, and
also among the M(r; m; n) when m = 5; 7 and 11. Some of the inequalities were conjectured by F. Garvan
in 1988, and myself in 1998.
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