The distribution of integer lengths of Klein polyhedra edges
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 214-221.

Voir la notice de l'article provenant de la source Math-Net.Ru

We examine some statistical properties for Klein polyhedra
@article{DVMG_2015_15_2_a5,
     author = {A. A. Illarionov},
     title = {The distribution of integer lengths of {Klein} polyhedra edges},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {214--221},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a5/}
}
TY  - JOUR
AU  - A. A. Illarionov
TI  - The distribution of integer lengths of Klein polyhedra edges
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2015
SP  - 214
EP  - 221
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a5/
LA  - ru
ID  - DVMG_2015_15_2_a5
ER  - 
%0 Journal Article
%A A. A. Illarionov
%T The distribution of integer lengths of Klein polyhedra edges
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2015
%P 214-221
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a5/
%G ru
%F DVMG_2015_15_2_a5
A. A. Illarionov. The distribution of integer lengths of Klein polyhedra edges. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 214-221. http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a5/

[1] F. Klein, “Uber eine geometrische Auffassung der gewohlichen Kettenbruchentwichlung”, Nachr. Ges. Wiss. Göttingem, 3 (1895), 357–359

[2] V. I. Arnold, “Preface”, Amer. Math. Soc. Transl., 197:2 (1999), ix–xii | MR

[3] V. I. Arnold, Zadachi Arnolda, Fazis, M., 2000 | MR

[4] O. N. Karpenkov, Geometry of Continued Fractions, Algorithms and Computation in Mathematics, 26, Springer-Verlag, Berlin Heidelberg, 2013 | DOI | MR | Zbl

[5] A. A. Illarionov, “Nekotorye svoistva trekhmernykh poliedrov Kleina”, Matem. sb., 206:4 (2015), 35–66 | DOI | MR | Zbl

[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 | MR

[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 | DOI | MR | Zbl

[8] E. N. Zhabitskaya, “Srednee znachenie summ nepolnykh chastnykh nepreryvnoi drobi”, Matem. zametki, 89:3 (2011), 472–476 | DOI | MR

[9] M. G. Rukavishnikova, “Zakon bolshikh chisel dlya summy nepolnykh chastnykh ratsionalnogo chisla s fiksirovannym znamenatelem”, Matem. zametki, 90:3 (2011), 431–444 | DOI | MR | Zbl

[10] A. A. Illarionov, “O statisticheskikh svoistvakh mnogogrannikov Kleina trekhmernykh tselochislennykh reshetok”, Matem. sb., 204:6 (2013), 23–46 | DOI | MR | Zbl

[11] A. A. Illarionov, D. A. Slinkin, “O kolichestve vershin mnogogrannikov Kleina v srednem”, Dalnevostochnyi matem. zhurn., 11:1 (2011) | MR

[12] V. A. Timorin, Kombinatorika vypuklykh mnogogrannikov, MTsNMO, M., 2002

[13] A. A. Illarionov, “On the Asymptotic Distribution of Integer Matrices”, Moscow Journal of Combinatorics and Number Theory, 1:4 (2011), 301–345 | MR