On partitioning Sidon sets with quasi-independent sets

Library card and held copy.

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K. J. Harrison and L. Thomas Ramsey, "On partitioning Sidon sets with quasi-independent sets," Colloquium Mathematicum 69 (1996), 117--131.

What the research consumes

The card carries the digest: the $N$-independence terminology, the random positive examples of Theorem 1, and the finite-determination results (Lemma 11 and Theorems 7 and 8). The paper's quasi-independence is dissociation in Problem 774.

The research uses the finite-determination principle. With $\mu(E,m)$ the least number of $m$-independent classes covering $E$, Lemma 11 gives $\mu(E,m)=\sup\{\mu(F,m):F\subset E\text{ finite}\}$, and Theorems 7 and 8 assemble finite examples of unbounded cover number at rapidly increasing scales while preserving a common Sidon bound. The random blocks of Theorem 1 have a uniformly bounded cover by design and are evidence for the positive side, not counterexamples. Reading depth is claims checked.