Finite unions of quasi-independent sets

Library card.

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David Grow and William C. Whicher, "Finite unions of quasi-independent sets," Canadian Mathematical Bulletin 27 (1984), 490–493; the card names the copy read, and no file is held.

What the research consumes

The card carries the digest: the fifteen-point example, the equivalence of the infinite covering question over $\mathbb Z$ with a uniform finite covering question, and the scale-separated block construction. The research consumes all three.

The example $E=\{3^j+kj:1\leq j\leq5,\ 0\leq k\leq2\}$, with hereditary extraction ratio two and no proper two-coloring, is verified exhaustively by the Grow–Whicher probe. The reduction to finite blocks, with the growth inequality displayed on printed p. 492, is restated and proved for positive integer blocks in the finite-block theorem. The paper's computation is not accompanied by its programs; the probe replaces it. Reading depth is claims checked, with the reduction reproved and the example recomputed here.