Naslov
Polarized Partitions and Partitions with d-distant Parts

Autori
Martinjak, Ivica

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
5th Polish Combinatorial Conference, Book of Abstracts / - , 2014

Skup
5th Polish Combinatorial Conference

Mjesto i datum
Będlewo, Poljska, 22.11.2014. - 26.11.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
partition identity ; direct bijection ; polarized partition ; Bressoud bijection

Sažetak
A partition with d-distant parts is the sequence \lambda=(\lambda_1, \lambda_2, ..., \lambda_l) with the constraint \lambda_i-\lambda_{; ; ; i+1}; ; ; \ge d. These partitions are generalization of partitions of Rogers-Ramanujan type. Partitions with 1-distant parts and with the property that the minimal even part is greater than double number of odd parts we call polarized. It is known that the number of polarized partitions \lambda \vdash n is equal to the number of partitions with 2-distant parts, as a specialization of a more general bijection (Bressoud, 1978). We prove that the number of partitions \lambda \vdash n with d-distant parts is equal to the number of polarized partitions \mu_i \vdash n-(d-2){; ; ; i \choose 2}; ; ; , with length equal to i, i \ge 1. As a consequence of this result, the number of partitions with d-distant parts is represented as the number of partitions of Rogers-Ramanujan type. Joint work with Dragutin Svrtan.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA