Geodesic
Coxeter transformations and the number~``$-1$''
Sbornik. Mathematics, Tome 191 (2000) no. 10, pp. 1471-1476

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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. 
@article{SM_2000_191_10_a3,
     author = {V. A. Kolmykov},
     title = {Coxeter transformations and the number~``$-1$''},
     journal = {Sbornik. Mathematics},
     pages = {1471--1476},
     publisher = {mathdoc},
     volume = {191},
     number = {10},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_10_a3/}
}
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V. A. Kolmykov. Coxeter transformations and the number~``$-1$''. Sbornik. Mathematics, Tome 191 (2000) no. 10, pp. 1471-1476. http://geodesic.mathdoc.fr/item/SM_2000_191_10_a3/