Problem dossier · Algebra
Rota's basis conjecture
Given n disjoint bases of an n-dimensional vector space (or rank-n matroid), the n² vectors can be arranged in an n×n grid whose every row and every column is a basis.
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Status
Open. Proved for n ≤ 4, for paving matroids and several other classes; online and fractional relaxations partially resolved.
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The Angle of Attack
Exhaustive verification over small matroids and random vector configurations; search for obstructions in the latin-square-like structure of partial arrangements.
Tags: matroids · bases · latin squares · linear algebra
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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