A Generalisation of Sperner's Theorem Using Weighted Chains

We find the (unique) largest subset of $\{0, 1, 2\}^n$ such that it contains no two elements, one of which is coordinatewise greater than the other, but strictly greater on at most $k$ coordinates. To do so, we decompose the cube into weighted chains. In Appendix B we present a new proof of Sperner's theorem we found while working on this problem.

Publication Details

Journal
ArXiv.org
Published
2025-09-30
Primary Topic
Protein Structure and Dynamics
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

A Generalisation of Sperner's Theorem Using Weighted Chains

ArXiv.org
Protein Structure and Dynamics
article

A Generalisation of Sperner's Theorem Using Weighted Chains

article en

Abstract

We find the (unique) largest subset of $\{0, 1, 2\}^n$ such that it contains no two elements, one of which is coordinatewise greater than the other, but strictly greater on at most $k$ coordinates. To do so, we decompose the cube into weighted chains. In Appendix B we present a new proof of Sperner's theorem we found while working on this problem.

ArXiv.org
Openalex Percentile: Top 47%
Protein Structure and Dynamics
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

A Generalisation of Sperner's Theorem Using Weighted Chains · ArXiv.org (2025) | TGRS Research Map | TGRS