Family 190CombinatoricsLeanNot yet digested
Polynomial removal fails for ordered binary matrices
Disproves polynomial ordered binary matrix removal with one fixed zero–one pattern. Matrices can require many binary-entry changes to become pattern-free while their copy density is smaller than every proposed polynomial bound in that distance. Copies preserve row and column orders and match both zeros and ones.
Manuscripts in this family · 1
Polynomial removal fails for ordered binary matrices
Sep 25, 2026·paper.pdfLean
We construct a fixed binary matrix for which ordered matrix removal has no polynomial bound. This disproves the polynomial ordered binary matrix-removal conjecture. Ordered copies preserve the separate row and column orders and match both zeros and ones; removal permits changing entries in either direction.