Harmonics on posets

Dennis Stanton

Research output: Contribution to journalArticle

20 Scopus citations

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 languageEnglish (US)
Pages (from-to)136-149
Number of pages14
JournalJournal of Combinatorial Theory, Series A
Volume40
Issue number1
DOIs
StatePublished - Sep 1985

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