𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Proof of Solomon's Rule

✍ Scribed by Stephanie van Willigenburg

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
104 KB
Volume
206
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We put forward a proof of Solomon's rule, in terms of matrices, for multiplication in the descent algebra of the symmetric group. Our proof exploits the graphs ÄŽ .4 ny 1 that we can obtain from all the subsets of the set of transpositions, i, i q 1 .

📜 SIMILAR VOLUMES

A proof of Solomon's second conjecture o
A proof of Solomon's second conjecture on local zeta functions of orders
✍ Osamu Iyama 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 111 KB

Throughout this paper, let R be a complete discrete valuation ring with the residue field k and the quotient field K, and Λ an R-order in a semisimple K-algebra A [CR]. We assume that k is a finite field with q elements. For an A-module V of finite length, we denote by L Λ (V ) the set of full Λ-lat

A Brauer Algebra Theoretic Proof of Litt
A Brauer Algebra Theoretic Proof of Littlewood's Restriction Rules
✍ Fabio Gavarini 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 278 KB

Let U be a complex vector space endowed with an orthogonal or symplectic Ž . Ž form, and let G be the subgroup of GL U of all the symmetrics of this form resp. . In this paper we give a new representation-G theoretic proof of this formula: realizing M in a tensor power U m f and using Schur's duali

Proof of the Hückel rule
Proof of the Hückel rule
✍ Ivan Gutman 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 166 KB

The HEckel rule is proved for an arbitrruy alternant system. Its validity is shown to be ïntimately related with the pairing theorem.

A simple proof for a simple rule
A simple proof for a simple rule
✍ A. Martín Sánchez; F. Vera Tomé 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 104 KB