The distribution of integer lengths of Klein polyhedra edges |
A.A. Illarionov |
2015, issue 2, P. 214-221 |
Abstract |
We examine some statistical properties for Klein polyhedra. |
Keywords: Klein polyhedra, multidimensional continued fractions |
Download the article (PDF-file) |
References |
[1] F. Klein, "Uber eine geometrische Auffassung der gewohlichen Kettenbruchentwichlung", Nachr. Ges. Wiss. Gottingem, 3 (1895), 357-359. [2] V.I. Arnold, "Preface", Amer. Math. Soc. Transl., 197:2 (1999), ix-xii. [3] V.I. Arnol'd, Zadachi Arnol'da, Fazis, M., 2000. [4] O.N. Karpenkov, Geometry of Continued Fractions, Algorithms and Computation in Mathematics, 26, Springer-Verlag, Berlin Heidelberg, 2013. [5] A.A. Illarionov, "Nekotorye svojstva trehmernyh polijedrov Klejna", Matem. sb., 206:4 (2015), 35-66. [6] H. Heilbronn, "On the average length of a class of finite continued fractions", Number Theory and Analysis, Papers in Honor of Edmund Landau, Plenum, New York, 1969, 87-96. [7] A.C. Yao, D.E. Knuth, "Analysis of the subtractive algorithm for greatest common divisors", Proc. Nat. Acad. Sci. USA, 72:12 (1975), 4720-4722. [8] E.N. Zhabickaja, "Srednee znachenie summ nepolnyh chastnyh nepreryvnoj drobi", Matem. zametki, 89:3 (2011), 472-476. [9] M.G. Rukavishnikova, "Zakon bol'shih chisel dlja summy nepolnyh chastnyh racional'nogo chisla s fiksirovannym znamenatelem", Matem. zametki, 90:3 (2011), 431-444. [10] A.A. Illarionov, "O statisticheskih svojstvah mnogogrannikov Klejna trehmernyh celochislennyh reshetok", Matem. sb., 204:6 (2013), 23-46. [11] A.A. Illarionov, D.A. Slinkin, "O kolichestve vershin mnogogrannikov Klejna v srednem", Dal'nevostochnyj matem. zhurn., 11:1 (2011). [12] V.A. Timorin, Kombinatorika vypuklyh mnogogrannikov, MCNMO, M., 2002. [13] A.A. Illarionov, "On the Asymptotic Distribution of Integer Matrices", Moscow Journal ofCombinatorics and Number Theory, 1:4 (2011), 301-345. |