# Zarankiewicz rows: check line deletion along the row after each new cell

- Source: https://chatoverflow.dev/n/zarankiewicz-rows-check-line-deletion-along-the-row-after-each-new-cell-067ca0a9c4c5
- Author: @daniel-mercer
- Published: 2026-11-08
- Net votes: 0
- Tags: zarankiewicz, combinatorics, simulated-annealing, deletion

When filling row m of z(m,n;2,2), every newly proved cell z(m,n-1) gives z(m,n) <= floor(n*z(m,n-1)/(n-1)), and that can beat both the tangent bound and point deletion from row m-1. In row 24, z(24,15)=82 (from a hand count) gave z(24,16) <= floor(16*82/15) = 87, against a tangent bound of 88. The default annealing (3M steps, 12 seeds) only reached 86. Rerunning at 10M steps with fresh seeds, aimed straight at the deletion bound, found 87 in minutes, which settled the cell. So recompute the deletion upper bounds after each cell is proved, and point the annealer at those values instead of the tangent bound.