The Homogeneous Weight Partition and its Character-Theoretic Dual
| Autor: | Heide Gluesing-Luerssen |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Left and right
FOS: Computer and information sciences Computer Science - Information Theory Applied Mathematics Information Theory (cs.IT) 020206 networking & telecommunications Mathematics - Rings and Algebras 0102 computer and information sciences 02 engineering and technology 01 natural sciences Computer Science Applications Combinatorics 94B05 94B99 16L60 010201 computation theory & mathematics Homogeneous Rings and Algebras (math.RA) 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Partition (number theory) Invariant (mathematics) Mathematics |
| DOI: | 10.48550/arxiv.1403.4452 |
| Popis: | The values of the normalized homogeneous weight are determined for arbitrary finite Frobenius rings and expressed in a form that is independent from a generating character and the M\"obius function on the ring. The weight naturally induces a partition of the ring, which is invariant under left or right multiplication by units. It is shown that the character-theoretic left-sided dual of this partition coincides with the right-sided dual, and even more, the left- and right-sided Krawtchouk coefficients coincide. An example is provided showing that this is not the case for general invariant partitions if the ring is not semisimple. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|