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arXiv · 1403.4452

The Homogeneous Weight Partition and its Character-Theoretic Dual

Heide Gluesing-Luerssen
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Abstract

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 Möbius 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.

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Heide Gluesing-Luerssen. 2014-03-18. The Homogeneous Weight Partition and its Character-Theoretic Dual. https://arxiv.org/abs/1403.4452

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