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Mat. Zametki, 2010, Volume 87, Issue 5, Pages 721–733 (Mi mz8720)  

This article is cited in 1 scientific paper (total in 1 paper)

Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis $\{&,\vee,\oplus,-\}$

O. V. Zubkov

Irkutsk State Pedagogical University

Abstract: We consider repetition-free Boolean functions in the basis $\{&,\vee,\oplus,-\}$, and prove a formula expressing the number of such functions of $n$ variables as a product of Fibonacci numbers. These products are estimated; as a result, we obtain asymptotic estimates for the number of repetition-free Boolean functions. These estimates involve Euler numbers of second order and can be reduced by well-known methods to the form of an exponential-power series. These estimates can be used to construct the final asymptotics of the number of repetition-free Boolean functions in the full binary basis.

Keywords: repetition-free Boolean function, full binary basis, binary function, Fibonacci numbers, Euler numbers, index preserving structure

DOI: https://doi.org/10.4213/mzm8720

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English version:
Mathematical Notes, 2010, 87:5, 687–699

Bibliographic databases:

UDC: 519.11+519.71
Received: 26.09.2008
Revised: 22.10.2009

Citation: O. V. Zubkov, “Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis $\{&,\vee,\oplus,-\}$”, Mat. Zametki, 87:5 (2010), 721–733; Math. Notes, 87:5 (2010), 687–699

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Voblyi, “On the asymptotics of the number of repetition-free Boolean functions in the basis $\{&,\lor,\oplus,\lnot\}$”, Discrete Math. Appl., 27:1 (2017), 55–56  mathnet  crossref  crossref  mathscinet  isi  elib
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