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Diskr. Mat., 2006, Volume 18, Issue 2, Pages 123–131 (Mi dm51)  

This article is cited in 3 scientific papers (total in 3 papers)

On the distribution of the number of ones in a Boolean Pascal's triangle

F. M. Malyshev, E. V. Kutyreva


Abstract: This research is devoted to estimating the number of Boolean Pascal's triangles of large enough size $s$ containing a given number of ones $\xi\le ks$, $k>0$. We demonstrate that any such Pascal's triangle contains a zero triangle whose size differs from $s$ by at most constant depending only on $k$. We prove that there is a monotone unbounded sequence of rational numbers $0=k_0<k_1<\dotsc$ such that the distribution of the number of triangles is concentrated in some neighbourhoods of the points $k_is$. The form of the distribution in each neighbourhood depends not on $s$ but on the residue of $s$ some modulo depending on $i\ge 0$.

DOI: https://doi.org/10.4213/dm51

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English version:
Discrete Mathematics and Applications, 2006, 16:3, 271–279

Bibliographic databases:

Received: 06.10.2004
Revised: 14.12.2005

Citation: F. M. Malyshev, E. V. Kutyreva, “On the distribution of the number of ones in a Boolean Pascal's triangle”, Diskr. Mat., 18:2 (2006), 123–131; Discrete Math. Appl., 16:3 (2006), 271–279

Citation in format AMSBIB
\Bibitem{MalKut06}
\by F.~M.~Malyshev, E.~V.~Kutyreva
\paper On the distribution of the number of ones in a Boolean Pascal's triangle
\jour Diskr. Mat.
\yr 2006
\vol 18
\issue 2
\pages 123--131
\mathnet{http://mi.mathnet.ru/dm51}
\crossref{https://doi.org/10.4213/dm51}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2283336}
\zmath{https://zbmath.org/?q=an:1128.60010}
\elib{http://elibrary.ru/item.asp?id=9311200}
\transl
\jour Discrete Math. Appl.
\yr 2006
\vol 16
\issue 3
\pages 271--279
\crossref{https://doi.org/10.1515/156939206777970435}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747495979}


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  • http://mi.mathnet.ru/eng/dm51
  • https://doi.org/10.4213/dm51
  • http://mi.mathnet.ru/eng/dm/v18/i2/p123

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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. F. M. Malyshev, “Bazisy rekurrentnykh posledovatelnostei”, Chebyshevskii sb., 16:2 (2015), 155–185  mathnet  elib
    2. F. M. Malyshev, “Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle”, Discrete Math. Appl., 27:3 (2017), 149–176  mathnet  crossref  crossref  mathscinet  isi  elib
    3. F. M. Malyshev, “Bulevy analogi treugolnika Paskalya s maksimalno vozmozhnym chislom edinits”, Diskret. matem., 32:1 (2020), 51–59  mathnet  crossref
  • Дискретная математика
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