The number of harmonic frames of prime order. (English) Zbl 1180.42019
Summary: Harmonic frames of prime order are investigated. The primary focus is the enumeration of inequivalent harmonic frames, with the exact number given by a recursive formula. The key to this result is a one-to-one correspondence developed between inequivalent harmonic frames and the orbits of a particular set. Secondarily, the symmetry group of prime order harmonic frames is shown to contain a subgroup consisting of a diagonal matrix as well as a permutation matrix, each of which is dependent on the particular harmonic frame in question.
MSC:
| 42C15 | General harmonic expansions, frames |
| 05A05 | Permutations, words, matrices |
| 20E07 | Subgroup theorems; subgroup growth |
References:
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