Binomial coefficient predictors

Vladimir Shevelev

Binomial coefficient predictors

Vladimir Shevelev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For a prime p and nonnegative integers n, k, consider the set A^(p) _n,k = {x ∈ [0, 1,..., n]: p^k{Pipe}{Pipe}(ⁿ _x)}. Let the expansion of n + 1 in base p be n + 1 = α0p^ν + α1p^ν-1 + · · · + α_ν, where 0 ≤ α_i ≤ p - 1, i = 0,..., ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if {Pipe}A^(p) _n,k{Pipe} = αkp^ν-k, k = 0, 1,..., ν. We give a full description of the p-BCP's in every base p.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Journal of Integer Sequences
Volume	14
Issue number	2
State	Published - 30 May 2011

Keywords

Binomial coefficient
Kummer's theorem
Maximal exponent of a prime dividing an integer
P-ary expansion of integer

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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title = "Binomial coefficient predictors",

abstract = "For a prime p and nonnegative integers n, k, consider the set A(p) n,k = \{x ∈ [0, 1,..., n]: pk\{Pipe\}\{Pipe\}(n x)\}. Let the expansion of n + 1 in base p be n + 1 = α0pν + α1pν-1 + · · · + αν, where 0 ≤ αi ≤ p - 1, i = 0,..., ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if \{Pipe\}A(p) n,k\{Pipe\} = αkpν-k, k = 0, 1,..., ν. We give a full description of the p-BCP's in every base p.",

keywords = "Binomial coefficient, Kummer's theorem, Maximal exponent of a prime dividing an integer, P-ary expansion of integer",

author = "Vladimir Shevelev",

year = "2011",

month = may,

day = "30",

language = "English",

volume = "14",

pages = "1--8",

journal = "Journal of Integer Sequences",

issn = "1530-7638",

publisher = "University of Waterloo",

number = "2",

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TY - JOUR

T1 - Binomial coefficient predictors

AU - Shevelev, Vladimir

PY - 2011/5/30

Y1 - 2011/5/30

N2 - For a prime p and nonnegative integers n, k, consider the set A(p) n,k = {x ∈ [0, 1,..., n]: pk{Pipe}{Pipe}(n x)}. Let the expansion of n + 1 in base p be n + 1 = α0pν + α1pν-1 + · · · + αν, where 0 ≤ αi ≤ p - 1, i = 0,..., ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if {Pipe}A(p) n,k{Pipe} = αkpν-k, k = 0, 1,..., ν. We give a full description of the p-BCP's in every base p.

AB - For a prime p and nonnegative integers n, k, consider the set A(p) n,k = {x ∈ [0, 1,..., n]: pk{Pipe}{Pipe}(n x)}. Let the expansion of n + 1 in base p be n + 1 = α0pν + α1pν-1 + · · · + αν, where 0 ≤ αi ≤ p - 1, i = 0,..., ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if {Pipe}A(p) n,k{Pipe} = αkpν-k, k = 0, 1,..., ν. We give a full description of the p-BCP's in every base p.

KW - Binomial coefficient

KW - Kummer's theorem

KW - Maximal exponent of a prime dividing an integer

KW - P-ary expansion of integer

UR - https://www.scopus.com/pages/publications/79957532508

M3 - Article

AN - SCOPUS:79957532508

SN - 1530-7638

VL - 14

SP - 1

EP - 8

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 2

ER -

Binomial coefficient predictors

Abstract

Keywords

ASJC Scopus subject areas

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