𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Extending Theorems of Göllnitz, A New Family of Partition Identities

✍ Scribed by JoséPlínio De O. Santos; Paulo Mondek

Book ID
110281337
Publisher
Springer US
Year
1999
Tongue
English
Weight
44 KB
Volume
3
Category
Article
ISSN
1382-4090

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

A Quartic Key Identity for a Partition T
A Quartic Key Identity for a Partition Theorem of Göllnitz
✍ Krishnaswami Alladi; George E. Andrews 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 144 KB

A key identity in three free parameters involving partitions into distinct parts is proved using Jackson's q-analog of Dougall's summation. This identity is shown to be combinatorially equivalent to a reformulation of a deep partition theorem of Go llnitz obtained by the use of a quartic transformat

A Computer Proof of a Polynomial Identit
A Computer Proof of a Polynomial Identity Implying a Partition Theorem of Göllnitz
✍ Alexander Berkovich; Axel Riese 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 117 KB

In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we provide computer proofs for new finite analogs of Jacobi and Euler formulas. All computer proofs are done with the aid of the new computer algebra packag

On a Partition Theorem of Göllnitz and Q
On a Partition Theorem of Göllnitz and Quartic Transformations
✍ Krishnaswami Alladi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 336 KB

For i=1, 2, 3, 4, let Q i (n) denote the number of partitions of n into distinct parts i (mod 4). New weighted identities in three free parameters are established connecting Q i (n) with partitions whose parts differ by 4 and such that consecutive members of the arithmetic progression #i (mod 4) can

A variation on a theme of Sylvester — a
A variation on a theme of Sylvester — a smoother road to Göllnitz's (Big) theorem
✍ Krishnaswami Alladi 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 698 KB

Using graphical representation, a simple bijective proof of the following result is given: 'The number of partitions of a positive integer n into distinct odd parts equals the number of partitions of n into parts # 2 and differing by > 6, where the inequality is strict if a part is even'. A threepar