![[Abstract]](http://www.math.ufl.edu/~frank/icons/scroll.gif)
Alexander Berkovich and Frank G. Garvan;
The GBG-Rank and t-Cores I. Counting and 4-Cores,
Journal of Combinatorics and Number Theory,
1 (2009), no. 3, 49--64.
Abstract:
Let rj(pi,s) denote the number of cells, colored j,
in the s-residue diagram of partition pi.
The GBG-rank of pi mod s is defined as
GBG-rank(pi,s) =
SUM j=0s-1
rj(pi,s) e2pi I j/s, I=sqrt(-1).
We will prove that for (s,t)=1
nu(s,t) < binomial(s+t,s)/(s+t),
where nu(s,t) denotes a number of distinct values that
the GBG-rank of a t-core mod s may assume.
The above inequality becomes an equality when s is prime or
when s is composite and t<2ps,
where ps is a smallest prime divisor of s.
We will show that the generating functions for 4-cores with
prescribed GBG-rank mod 3 value are all
eta-products.
The url of this page is http://www.math.ufl.edu/~frank/abstracts/GBG.html.
Created by
F.G. Garvan
(fgarvan@ufl.edu) on
Wednesday, August 13, 2008.
Last update made Tue Oct 6 13:40:54 EDT 2009.
fgarvan@ufl.edu
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