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Mat. Sb., 2000, Volume 191, Number 10, Pages 51–56 (Mi msb515)  

This article is cited in 5 scientific papers (total 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.

DOI: https://doi.org/10.4213/sm515

Full text: PDF file (194 kB)
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English version:
Sbornik: Mathematics, 2000, 191:10, 1471–1476

Bibliographic databases:

UDC: 512.543.14+512.643.5+512.817.73
MSC: Primary 05C50; Secondary 05C05
Received: 12.07.1999

Citation: V. A. Kolmykov, “Coxeter transformations and the number “$-1$””, Mat. Sb., 191:10 (2000), 51–56; Sb. Math., 191:10 (2000), 1471–1476

Citation in format AMSBIB
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\paper Coxeter transformations and the number~``$-1$''
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\vol 191
\issue 10
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\issue 10
\pages 1471--1476
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Kolmykov, “Coxeter transformations and spectra of operations”, Sb. Math., 193:3 (2002), 345–357  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. A. Kolmykov, “Reflections and Three-Dimensionality”, Math. Notes, 73:6 (2003), 802–805  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. A. Kolmykov, “Coxeter transformation: Density Theorems”, Math. Notes, 76:1 (2004), 133–136  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. A. Kolmykov, “The Coxeter transformation: deltoids, trefoils, and decay numbers”, Sb. Math., 196:1 (2005), 63–75  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. V. A. Kolmykov, “Coxeter transformations: Construction of deltoids”, Math. Notes, 79:5 (2006), 643–648  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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