This article is cited in 5 papers

Coxeter transformations and the number "$-1$"

V. A. Kolmykov

Voronezh State University

Abstract: Coxeter transformations associated with trees are considered. The number "$-1$" plays an exceptional role with respect to the spectra of trees. The sets of all trees containing and not containing "$-1$" in the spectrum are studied. Their densities are determined, systems of generating elements and operations are found, and the properties of the edges of trees from these sets are studied.

UDC: 512.543.14+512.643.5+512.817.73

MSC: Primary 05C50; Secondary 05C05

Received: 12.07.1999

DOI: 10.4213/sm515

 English version: Sbornik: Mathematics, 2000, 191:10, 1471–1476

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