Infinite Families of Partitions into MSTD Subsets
Hung Viet Chu, Noah Luntzlara, Steven J. Miller, Lily Shao

TL;DR
This paper develops an efficient method to partition large initial segments of natural numbers into multiple MSTD subsets, addressing open questions about explicit decompositions and bounds on the minimal segment size for such partitions.
Contribution
It introduces a constructive approach for partitioning sets into multiple MSTD subsets and establishes bounds on the minimal size needed for these partitions.
Findings
Provided an explicit method for partitioning into k MSTD subsets for large r.
Established bounds for the minimal r (R(k)) for such partitions to exist.
Identified conditions for a positive proportion of such partitions as r grows.
Abstract
A set is MSTD (more-sum-than-difference) if . Though MSTD sets are rare, Martin and O'Bryant proved that there exists a positive constant lower bound for the proportion of MSTD subsets of as . Later, Asada et al. showed that there exists a positive constant lower bound for the proportion of decompositions of into two MSTD subsets as . However, the method is probabilistic and does not give explicit decompositions. Continuing this work, we provide an efficient method to partition (for sufficiently large) into MSTD subsets, positively answering a question raised by Asada et al. as to whether this is possible for all such . Next, let be the smallest integer such that for all , can be -decomposed into MSTD subsets. We…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRough Sets and Fuzzy Logic
