PreprintCC BY 4.0arXiv
Solution Space Partitioning for Extremal Set Theory
Abstract
We present a method for partitioning the solution space of statements in extremal set theory. Compared with domain-agnostic partitioning methods like look-ahead, we perform case analysis on the strategies by which a candidate solution can be constructed. We demonstrate that our approach can decompose problems in extremal set theory more effectively than look-ahead. Combining this new partitioning strategy with an exact proof-producing MILP solver, we are able to verify larger finite cases of Chvátal's Conjecture---a long-standing open question in extremal combinatorics---compared to previous work.
Versions
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BibTeX
@misc{looney2026solution,
title = {{Solution Space Partitioning for Extremal Set Theory}},
author = {Jesse Looney and Jonah McDonald and Allison Klingler and Gloria Wu and Jonad Pulaj and Haoze Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.06432},
eprint = {2608.06432},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06432},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Solution Space Partitioning for Extremal Set Theory
AU - Jesse Looney
AU - Jonah McDonald
AU - Allison Klingler
AU - Gloria Wu
AU - Jonad Pulaj
AU - Haoze Wu
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2608.06432
UR - https://arxiv.org/abs/2608.06432
AB - We present a method for partitioning the solution space of statements in extremal set theory. Compared with domain-agnostic partitioning methods like look-ahead, we perform case analysis on the strategies by which a candidate solution can be constructed. We demonstrate that our approach can decompose problems in extremal set theory more effectively than look-ahead. Combining this new partitioning strategy with an exact proof-producing MILP solver, we are able to verify larger finite cases of Chvátal's Conjecture---a long-standing open question in extremal combinatorics---compared to previous work.
ER -