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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 3(28), Pages 163–169 (Mi vsgtu1099)  

This article is cited in 5 scientific papers (total in 5 papers)

Discrete Mathematics

Reduction of the sum of the weight equal powers to explicit combinatorial representation

A. I. Nikonov

Samara State Technical University, Samara, Russia

Abstract: The paper contains the proof of the statement that the component of the sum of weighted powers with natural bases and equal parameters, dependent on weight coefficients, is equal to the sum of products of binomial and weight coefficients. It is proved also, that the component of this sum, independent of weight coefficients, is the algebraic sum of products of binomial coefficients and powers of natural numbers. Explicit combinatorial representation of the sum of the weighted equal powers contains the magnitudes taken from proved equalities.

Keywords: sum of weighted equal powers, combinatorial representation, binomial coefficients, weight coefficients

DOI: https://doi.org/10.14498/vsgtu1099

Full text: PDF file (131 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 512.14
MSC: 05A10
Original article submitted 26/VI/2012
revision submitted – 16/VII/2012

Citation: A. I. Nikonov, “Reduction of the sum of the weight equal powers to explicit combinatorial representation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(28) (2012), 163–169

Citation in format AMSBIB
\Bibitem{Nik12}
\by A.~I.~Nikonov
\paper Reduction of the sum of the weight equal powers to explicit combinatorial representation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 3(28)
\pages 163--169
\mathnet{http://mi.mathnet.ru/vsgtu1099}
\crossref{https://doi.org/10.14498/vsgtu1099}
\zmath{https://zbmath.org/?q=an:1326.05005}


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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. A. I. Nikonov, “Shifrovanie na osnove summ so slagaemymi — proizvedeniyami vesovykh i svobodnykh komponentov”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(29) (2012), 199–206  mathnet  crossref
    2. A. I. Nikonov, “Usloviya vydelimosti vesovykh koeffitsientov iz summ s chlenami posledovatelnostei dvukh vidov”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(31) (2013), 91–100  mathnet  crossref  elib
    3. A. I. Nikonov, “Kombinatornoe predstavlenie summy vzveshennykh odinakovykh stepenei chlenov arifmeticheskoi progressii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(33) (2013), 184–191  mathnet  crossref  zmath  elib
    4. A. I. Nikonov, “Povyshenie effektivnosti shifrovaniya na osnove summirovaniya proizvedenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(35) (2014), 199–207  mathnet  crossref  zmath
    5. A. I. Nikonov, “Summirovanie na osnove kombinatornogo predstavleniya odinakovykh stepenei”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 149–157  mathnet  crossref  zmath  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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