Naslov
Families of Identities for Integer Partitions and Partitions with Fixed Length

Autori
Martinjak, Ivica

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

Izvornik
Elementare and Analytische Zahlentheorie / - , 2014

Skup
Elementare and Analytische Zahlentheorie

Mjesto i datum
Hildesheim, Njemačka, 28.07.2014. - 01.08.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
partition identity ; direct bijection

Sažetak
The sequence of non-negative integers in weakly decreasing order is called a partition. In particular, it is said that a partition has d-distant parts if the minimal difference between consecutive parts is d. Let p(n) denotes the partition function. We demonstrate that the number of partitions of $n$ is equal to the number of partitions of 2n+d{; ; ; n \choose 2}; ; ; with n d-distant parts. Moreover, for every n, d \in {; ; ; \mathbb N}; ; ; _0 there are infinitely many sets of partitions whose length is a multiple of n and whose parts are d-distant, that are equinumerous to p(n). We also provide a bijective proof for this identity (Martinjak-Svrtan, 2014).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA