PreprintCC BY-ND 4.0HAL
MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS
Abstract
An addition chain of length h that leads to a number n is a sequence of positive integers s0=1,s1=2,…,sh=n such that si=sj+sk~(i>j≥ k) for each 1≤ i≤ h. We introduce a matrix-theoretic framework for studying the properties of arbitrary addition chains that lead to a target integer n≥ 2 by associating each chain and the sequence of dominant and lower weight summands that calculate each term in the chain an adjacency matrix that encodes the internal geometry. In this linear-algebraic and matrix theoretic framework, we investigate how rank, rank profiles, singular values, eigenvalues, matrix norms, predecessor depths, and track-interaction terms encode the combinatorial and arithmetic structure of addition chains
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BibTeX
@misc{agama2026matrix,
title = {{MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS}},
author = {Theophilus Agama},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05763442v1},
note = {CC BY-ND 4.0},
}
RIS
TY - UNPB
TI - MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS
AU - Theophilus Agama
PY - 2026
DA - 2026/09/24
PB - HAL
UR - https://hal.science/hal-05763442v1
AB - An addition chain of length h that leads to a number n is a sequence of positive integers s_0=1,s_1=2,…,s_h=n such that s_i=s_j+s_k~(i>j≥ k) for each 1≤ i≤ h. We introduce a matrix-theoretic framework for studying the properties of arbitrary addition chains that lead to a target integer n≥ 2 by associating each chain and the sequence of dominant and lower weight summands that calculate each term in the chain an adjacency matrix that encodes the internal geometry. In this linear-algebraic and matrix theoretic framework, we investigate how rank, rank profiles, singular values, eigenvalues, matrix norms, predecessor depths, and track-interaction terms encode the combinatorial and arithmetic structure of addition chains
ER -