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

S. P. Glasby, G. R. Paseman

Research output: Contribution to journalArticlepeer-review

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 → ∞.

Original languageEnglish
Article numberP2.5
Number of pages11
JournalElectronic Journal of Combinatorics
Volume29
Issue number2
DOIs
Publication statusPublished - 2022

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