PreprintCC BY-ND 4.0HAL
COUNTING FIXED DEGREE d ≥ 2 ADDITION CHAINS
Abstract
We denote the length of an addition chain with fixed degree d≥ 2 leading to n by ld(n). We study the counting function Fd(m,r):=#{n∈[dm,dm+1) : ld(n)≤ m+r} establishing upper and lower bounds, which generalizes previous classical investigations of De Koninck, Doyon, and Verreault
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BibTeX
@misc{agama2026counting,
title = {{COUNTING FIXED DEGREE d ≥ 2 ADDITION CHAINS}},
author = {Theophilus Agama},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05756229v1},
note = {CC BY-ND 4.0},
}
RIS
TY - UNPB
TI - COUNTING FIXED DEGREE d ≥ 2 ADDITION CHAINS
AU - Theophilus Agama
PY - 2026
DA - 2026/09/20
PB - HAL
UR - https://hal.science/hal-05756229v1
AB - We denote the length of an addition chain with fixed degree d≥ 2 leading to n by l^d(n). We study the counting function F_d(m,r):=#{n∈[d^m,d^m+1) : l^d(n)≤ m+r} establishing upper and lower bounds, which generalizes previous classical investigations of De Koninck, Doyon, and Verreault
ER -