Naslov
Identities for the Polarized Partitions and Partitions of Rogers-Ramanujan Type

Autori
Martinjak, Ivica

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
2nd Algorithmic and Enumerative Combinatorics Summer School 2015

Mjesto i datum
Linz, Austrija, 27.07.2015. - 31.07.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
partition identity ; direct bijection ; polarized partition ; partition of Rogers-Ramanujan type

Sažetak
Let $e(\lambda)$ be the smallest even part of a partition $\lambda \vdash n$ or, in case of a partition with all parts odd, we set $e(\lambda):=2l_o(\lambda)+2$ where $l_o(\lambda)$ is the number of odd parts in a partition. Partitions with distant parts and obeying the property $e(\lambda) > 2l_o(\lambda)$ we shall call {; ; \it polarized partitions}; ; . The number of partitions $\lambda \vdash n$ with $2$-distant parts is equal to the number of polarized partitions $\mu \vdash n$, $p^{; ; (2)}; ; (n)=\hat{; ; p}; ; ^{; ; (1)}; ; (n)$ \cite{; ; Bress}; ; . In this work we present a new family of integer partition identities \cite{; ; MaSv}; ; . The number of partitions with $d$-distant parts can be written as a sum of the numbers of partitions of various lengths with 1-distant parts whose even parts, if there are any, are greater than twice the number of odd parts, p^{; ; (d)}; ; (n)= \sum_{; ; i \ge 1 }; ; \hat{; ; p}; ; ^{; ; (1)}; ; _i(n- (d-2){; ; i \choose 2}; ; ). We also show that the number of partitions with $d$-distant parts can be written as a sum of numbers of partitions of {; ; \it Rogers-Ramanujan type}; ; of various lengths. Joint work with Dragutin Svrtan.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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