This article is cited in 2 papers

Reflections and Three-Dimensionality

V. A. Kolmykov

Voronezh State University

Abstract: If the dimension of a linear space is not greater than 3, then the characteristic polynomial of the Coxeter transformation associated with any symmetric matrix is invariant under the natural action of the symmetric group. If the dimensionality is greater than 3, then this statement does not hold. The set of all trees such that the spectrum of their associated Coxeter transformation contains negative one is three-dimensional.

UDC: 512.543.14+512.643.5+512.817.73

Received: 14.01.2002

DOI: 10.4213/mzm232

 English version: Mathematical Notes, 2003, 73:6, 802–805

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