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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2012, Issue 3(28), Pages 163–169
DOI: https://doi.org/10.14498/vsgtu1099 (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
Full-text PDF (131 kB) Citations (5)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1099
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.
Original article submitted 26/VI/2012
revision submitted – 16/VII/2012
Bibliographic databases:
Document Type: Article
UDC: 512.14
MSC: 05A10
Language: Russian
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}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu1099
  • https://www.mathnet.ru/eng/vsgtu/v128/p163
    • This publication is cited in the following 5 articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    References:60
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