Schur degrees of block sums

What is the Schur degree L(n) of block sums? Eliahou and Revuelta conjectured L(n)=S(n−1)+1, linking it to Schur numbers; the unresolved first cases included L(4) and L(5).

Why it matters and what counts as progress

Why it matters: The first unsettled block-sum cases test a proposed relation between block sums and classical Schur numbers.

What counts as progress: Determine L(n) exactly, improve lower bounds through sumfree covers, or disprove the proposed relation at another n.

How the problem developed

2 Jun 2020 · Conjecture [1]
Shalom Eliahou and Juan Revuelta Defined Schur degree and conjectured L(n)=S(n−1)+1 for block sums, including predictions L(4)=14 and L(5)=45.
26 Sept 2026 · Counterexample [2]
Schur-degree block-sums project authors Proved L(4)=16 and L(5)≥49, refuting the stated formula at n=4 and n=5.