A Computational Approach to Square Graham Partitions

Byungchan Kim; Eunmi Kim; Yoon Kyung Park

doi:10.1080/10586458.2025.2484445

A Computational Approach to Square Graham Partitions

School of Natural Sciences

Ewha Womans University

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

Abstract

We propose an algorithm based on Monte Carlo Tree Search equipped with a supervised learned neural network to find an integer partition of n into squares satisfying (Formula presented.) with squares (Formula presented.). By using induction and the search algorithm, we prove that such a partition exists if (Formula presented.).

Original language	English
Journal	Experimental Mathematics
DOIs	https://doi.org/10.1080/10586458.2025.2484445
State	Accepted/In press - 2025

Keywords

MCTS
neural network
square Graham partition

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10.1080/10586458.2025.2484445

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title = "A Computational Approach to Square Graham Partitions",

abstract = "We propose an algorithm based on Monte Carlo Tree Search equipped with a supervised learned neural network to find an integer partition of n into squares satisfying (Formula presented.) with squares (Formula presented.). By using induction and the search algorithm, we prove that such a partition exists if (Formula presented.).",

keywords = "MCTS, neural network, square Graham partition",

author = "Byungchan Kim and Eunmi Kim and Park, \{Yoon Kyung\}",

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year = "2025",

doi = "10.1080/10586458.2025.2484445",

language = "English",

journal = "Experimental Mathematics",

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T1 - A Computational Approach to Square Graham Partitions

AU - Kim, Byungchan

AU - Kim, Eunmi

AU - Park, Yoon Kyung

PY - 2025

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AB - We propose an algorithm based on Monte Carlo Tree Search equipped with a supervised learned neural network to find an integer partition of n into squares satisfying (Formula presented.) with squares (Formula presented.). By using induction and the search algorithm, we prove that such a partition exists if (Formula presented.).

KW - MCTS

KW - neural network

KW - square Graham partition

UR - https://www.scopus.com/pages/publications/105002591788

U2 - 10.1080/10586458.2025.2484445

DO - 10.1080/10586458.2025.2484445

M3 - Article

AN - SCOPUS:105002591788

SN - 1058-6458

JO - Experimental Mathematics

JF - Experimental Mathematics

ER -

A Computational Approach to Square Graham Partitions

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Keywords

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