• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Геометрическое доказательство формулы Рёдсета для чисел Фробениуса
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
October 1, 2026
HSE Researchers Show How Congenital Motor Disorders Affect Brain Development
Researchers from HSE University’s Institute for Cognitive Neuroscience have synthesised the findings of their previous studies on brain development in children with obstetric brachial plexus palsy and arthrogryposis. Their analysis shows that impaired motor function in early childhood not only limits children’s motor experience but also affects memory, categorical thinking, and information processing. The study has been published in Frontiers in Psychology.
October 1, 2026
Window into the Body: Scientists Develop Neural Network to Detect Risk of 15 Diseases from Retinal Images
Russian universities, with the participation of HSE University, Sber, and Z-union, have developed a neural network that can simultaneously assess the risk of 15 types of pathology from retinal photographs, including not only eye diseases but also cardiovascular conditions. The AI system can help clinicians detect potentially concerning changes at an early stage, identify signs reflecting the condition of retinal blood vessels, and determine whether a patient may need further examination. The paper has been published in Frontiers in Medicine.
September 30, 2026
'We Did Not Limit the Time for Questions'
The International Laboratory for Supercomputer Atomistic Modelling and Multi-Scale Analysis at HSE University held a major conference on molecular dynamics. Participants had the opportunity to attend all the presentations, while speakers were given as much time as they needed to answer questions. The HSE News Service interviewed Grigory Smirnov, Head of the Laboratory, and Genri Norman, Chief Research Fellow, about the conference preparations and the discussions it generated.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Геометрическое доказательство формулы Рёдсета для чисел Фробениуса

Труды Математического института им. В.А. Стеклова РАН. 2012. Т. 276. С. 280–287.
Ustinov A.

Using a geometric interpretation of continued fractions, we give a new proof of Rødseth's formula for Frobenius numbers.

Language: Russian
DOI
Text on another site
Keywords: Frobenius numbersЧисла Фробенисуа
Similar publications
Limiting distribution of Frobenius numbers for n = 3
Shchur V., Sinai Y. G., Ustinov A., Journal of Number Theory 2009 Vol. 129 No. 11 P. 2778–2789
The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers outlined in earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses. ...
Added: October 12, 2025
Решение задачи Арнольда о слабой асимптотике для чисел Фробениуса с тремя аргументами
Ustinov A., Математический сборник 2009 Т. 200 № 4 С. 131–160
It is shown that on the average the Frobenius numbers f(a,b,c) behave like 8/π√abc . ...
Added: October 11, 2025
О распределении чисел Фробениуса с тремя аргументами
Ustinov A., Известия РАН. Серия математическая 2010 Т. 74 № 5 С. 145–170
We prove the existence of the limit density distribution for normalized Frobenius numbers with three arguments. The density is found explicitly. ...
Added: October 9, 2025
Some properties of Frobenius numbers and a fraction of symmetric semigroups in the weak limit for n=3
Shchur V., Functional Analysis and Other Mathematics 2010 Vol. 3 No. 1 P. 97–101
We generalize and prove a conjecture by V.I. Arnold on the parity of Frobenius numbers. For the case of symmetric semigroups with three generators we give an exact formula for Frobenius numbers, which is, in a sense, a sum of two Sylvester’s formulae. We prove that a fraction of symmetric semigroups vanishes in the weak ...
Added: December 18, 2018
Limiting distribution of Frobenius numbers for n=3
Shchur V., Sinai Y., Ustinov A., Journal of Number Theory 2009 Vol. 129 No. 11 P. 2778–2789
The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers with three arguments outlined in the earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses. ...
Added: December 18, 2018
Среднее значение чисел Фробениуса с тремя аргументами
Frolenkov D., Известия РАН. Серия математическая 2012 Т. 76 № 4 С. 125–184
We get an asymptotic formula for the mean value of Frobenius numbers wiyh three arguments when averaged with respect to three parameters ...
Added: November 1, 2014
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit