𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Powers of Euler's Product and Related Identities

✍ Scribed by Shaun Cooper; Michael D. Hirschhorn; Richard Lewis

Book ID
110281672
Publisher
Springer US
Year
2000
Tongue
English
Weight
80 KB
Volume
4
Category
Article
ISSN
1382-4090

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πŸ“œ SIMILAR VOLUMES

Multiplicative Relations in Powers of Eu
Multiplicative Relations in Powers of Euler's Product
✍ Scott Ahlgren πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 133 KB

In a recent paper, Cooper, Hirschhorn, and Lewis conjecture many relations among the coefficients of certain products of powers of Euler's product. Here we use the theory of modular forms with complex multiplication to prove these conjectures.

Euler's relation, mΓΆbius functions and m
Euler's relation, mΓΆbius functions and matroid identities
✍ Raul Cordovil; Michel Vergnas; Arnaldo Mandel πŸ“‚ Article πŸ“… 1982 πŸ› Springer 🌐 English βš– 620 KB

We give a short combinatorial proof of the Euler relation for convex polytopes in the context of oriented matroids. Using counting arguments we derive from the Euler relation several identities holding in the lattice of flats of an oriented matroid. These identities are proven for any matroid by M6b