The GBG-Rank and t-Cores I. Counting and 4-Cores
| dc.creator | Berkovich, Alexander | |
| dc.creator | Garvan, Frank G. | |
| dc.date | 2008-07-30 | |
| dc.date | 2008-08-14 | |
| dc.date.accessioned | 2026-07-07T09:56:22Z | |
| dc.date.available | 2026-07-07T09:56:22Z | |
| dc.description | Let r_j(π,s) denote the number of cells, colored j, in the s-residue diagram of partition π. The GBG-rank of πmod s is defined as r_0+r_1*w_s+r_2*w_s^2+...+r_(s-1)*w_s^(s-1), where w_s=exp(2*Π*I/s). We will prove that for (s,t)=1, v(s,t) <= binomial(s+t,s)/(s+t), where v(s,t) denotes a number of distinct values that GBG-rank mod s of t-core may assume. The above inequality becomes an equality when s is prime or when s is composite and t<=2p_s, where p_s is a smallest prime divisor of s. We will show that the generating functions for 4-cores with the prescribed values of GBG-rank mod 3 are all eta-products. | |
| dc.description | 15 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0807.4727 | |
| dc.identifier | http://arxiv.org/abs/0807.4727 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166955 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11P81, 11P83, 05A17, 05A19 | |
| dc.title | The GBG-Rank and t-Cores I. Counting and 4-Cores | |
| dc.type | text |