On the maximum of the weighted r! " #m binomial sum 2−r i i=0

S. P. Glasby; G. R. Paseman

doi:10.37236/10751

On the maximum of the weighted r! " #_m binomial sum 2^−r i i=0

S. P. Glasby, G. R. Paseman

Mathematics and Statistics

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

3 Citations (Scopus)

Abstract

The weighted binomial sum f_m(r) = 2^−r!r "_m # i=0 i arises in coding theory and information theory. We prove that, for m ∕∈ {0, 3, 6, 9, 12}, the maximum value of f_m(r) with 0 ! r ! m occurs " when r = ⌊m/3⌋ + 1. We also show this maximum 3 value is asymptotic to √_3m πm 2# as m → ∞.

Original language	English
Article number	P2.5
Number of pages	11
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	2
DOIs	https://doi.org/10.37236/10751
Publication status	Published - 2022

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abstract = "The weighted binomial sum fm(r) = 2−r!r {"}m # i=0 i arises in coding theory and information theory. We prove that, for m ∕∈ {0, 3, 6, 9, 12}, the maximum value of fm(r) with 0 ! r ! m occurs {"} when r = ⌊m/3⌋ + 1. We also show this maximum 3 value is asymptotic to √3m πm 2# as m → ∞.",

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AU - Paseman, G. R.

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N2 - The weighted binomial sum fm(r) = 2−r!r "m # i=0 i arises in coding theory and information theory. We prove that, for m ∕∈ {0, 3, 6, 9, 12}, the maximum value of fm(r) with 0 ! r ! m occurs " when r = ⌊m/3⌋ + 1. We also show this maximum 3 value is asymptotic to √3m πm 2# as m → ∞.

AB - The weighted binomial sum fm(r) = 2−r!r "m # i=0 i arises in coding theory and information theory. We prove that, for m ∕∈ {0, 3, 6, 9, 12}, the maximum value of fm(r) with 0 ! r ! m occurs " when r = ⌊m/3⌋ + 1. We also show this maximum 3 value is asymptotic to √3m πm 2# as m → ∞.

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On the maximum of the weighted r! " #_m binomial sum 2^−r i i=0

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Complexity of group algorithms and statistical fingerprints of groups

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On the maximum of the weighted r! " #m binomial sum 2−r i i=0

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Complexity of group algorithms and statistical fingerprints of groups

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On the maximum of the weighted r! " #_m binomial sum 2^−r i i=0