### Abstract

Given a finite ranked poset P, for each rank of P a space of complex valued functions on P called harmonics is defined. If the automorphism group G of P is sufficiently rich, these harmonic spaces yield irreducible representations of G. A decomposition theorem, which is analogous to the decomposition theorem for spherical harmonics, is stated. It is also shown that P can always be decomposed into posets whose principal harmonics are orthogonal polynomials. Classical examples are given.

Original language | English (US) |
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Pages (from-to) | 136-149 |

Number of pages | 14 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1985 |

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## Cite this

Stanton, D. (1985). Harmonics on posets.

*Journal of Combinatorial Theory, Series A*,*40*(1), 136-149. https://doi.org/10.1016/0097-3165(85)90052-4