Displaying similar documents to “Flexary Operations”

Euler’s Partition Theorem

Karol Pąk (2015)

Formalized Mathematics

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In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].

Some finite generalizations of Euler's pentagonal number theorem

Ji-Cai Liu (2017)

Czechoslovak Mathematical Journal

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Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.

Combinatorial interpretations for identities using chromatic partitions

Mateus Alegri, Wagner Ferreira Santos, Samuel Brito Silva (2021)

Czechoslovak Mathematical Journal

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We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities.