Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Set systems
L214_spread_intersecting_families/: For every integer rho >= 2 an explicit intersecting family of n-sets is rho-spread under its uniform measure, with log2 n about rho (log2 rho)^2, and has absolutely r-spread subfamilies for every r >= 16. This explicit substitution construction gives an obstruction to constant-spread matching.
L215_spread_large_core_sunflowers/: For every real R >= 3 and integer g >= 0 an explicit intersecting family is R-spread under its uniform measure while every k-sunflower in it, for every k >= 3, has a core of at least 2^g points; no bounded-core sunflower lemma follows from spread.
L268_linear_word_sunflowers/: A linear word space of dimension at least sn contains an s-dimensional subspace whose coordinate maps are zero or injective. Consequently an affine linear word family without a k-sunflower has fewer than k^(2n) members, uniformly over finite fields and coordinate alphabet dimensions.
Each claim states its conventions, hypotheses and conclusion, with its proof and evidence standing on the card. The two spread claims concern the sunflower problem through the spread-family method: the first shows that spread does not force two disjoint members, and the second that it does not force a sunflower with a bounded core. Their research context is the sunflower exponential-bound folder.