Source notes for Problem 774

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alon: Source notes for Problem 774: An application of graph theory to additive number theory.

anderson: Source notes for Problem 774: Anderson: vectors of matroids over tracts.

bzdega: Source notes for Problem 774: Bounds on ternary cyclotomic coefficients.

christie: Source notes for Problem 774: Christie–Dykema–Klep: minimal vanishing sums of roots of unity.

conway_jones: Source notes for Problem 774: Conway–Jones: trigonometric Diophantine equations and vanishing sums.

coppersmith_steinberger: Source notes for Problem 774: Coppersmith–Steinberger: entry sums of cyclotomic arrays.

dadderio_moci: Source notes for Problem 774: D'Adderio–Moci: arithmetic matroids.

duval: Source notes for Problem 774: Duval–Klivans–Martin: cuts and flows of cell complexes.

edmonds: Source notes for Problem 774: Edmonds: partitioning a matroid into independent sets.

graham_leeb_rothschild: Source notes for Problem 774: Graham–Leeb–Rothschild: Ramsey theorem for classes of partitions.

graham_rothschild: Source notes for Problem 774: Graham–Rothschild: Ramsey theorem for parameter sets.

grow: Source notes for Problem 774: Finite unions of quasi-independent sets.

hare: Source notes for Problem 774: Sidon sets are proportionally Sidon with small Sidon constants.

harrison: Source notes for Problem 774: On partitioning Sidon sets with quasi-independent sets.

hindman_strauss: Source notes for Problem 774: A simple characterization of sets satisfying the Central Sets Theorem.

karagiannis: Source notes for Problem 774: Karagiannis: a combinatorial infinite Hales–Jewett proof.

lam_leung: Source notes for Problem 774: Lam–Leung: vanishing sums of roots of unity.

lewko: Source notes for Problem 774: The Sidon Decomposition Problem in Abelian Groups of Bounded Torsion.

lovitz_petrov: Source notes for Problem 774: A generalization of Kruskal's theorem on tensor decomposition.

martin_reiner: Source notes for Problem 774: Martin–Reiner: cyclotomic and simplicial matroids.

moser_tardos: Source notes for Problem 774: A constructive proof of the general Lovasz Local Lemma.

nesetril: Source notes for Problem 774: On Pisier Type Theorems.

onn: Source notes for Problem 774: Onn: convex discrete optimization.

pisier: Source notes for Problem 774: Arithmetic characterizations of Sidon sets.

poonen_rubinstein: Source notes for Problem 774: The Number of Intersection Points Made by the Diagonals of a Regular Polygon.

promel_voigt: Source notes for Problem 774: Prömel–Voigt: canonical partition theorems for parameter sets.

ramsey_graham: Source notes for Problem 774: Ramsey–Graham: planar Sidonicity and quasi-independence.

ramsey_graham_extension: Source notes for Problem 774: Ramsey–Graham: permutation and extension.

revesz_open_problems: Source notes for Problem 774: Problèmes ouverts: Théorie analytique des polynômes et analyse harmonique.

steinberger: Source notes for Problem 774: Steinberger: low-degree nonnegative cyclotomic multiples.

tan_zhang: Source notes for Problem 774: Tan–Zhang: nonnegative cyclotomic multiples.

tao_notes: Source notes for Problem 774: 254A, Notes 1: Elementary multiplicative number theory.

voigt: Source notes for Problem 774: Voigt: canonizing partition theorems.

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These notes summarize the sources used in the research. Follow the links to canonical library records for retained reading copies and bibliographic details.

Core problem sources

• pisier: equivalence between Sidonicity and proportional extraction of quasi-independent subsets.
• harrison: finite-block reduction and separated assembly.
• grow: the finite obstruction at extraction ratio one half.
• nesetril: fixed-order counterexamples and carry-free integer encoding.
• hare, lewko, alon: nearby positive results and boundary cases.

Roots-of-unity and matroid sources

• ramsey-graham: closest source; spike/shadow machinery and the explicit $T_{105},T_{165},T_{195}$ test cases.
• ramsey-graham-extension: coordinatewise symmetries and prime-extension results.
• martin-reiner, duval: cyclotomic/simplicial matroid dictionary and the coefficient obstruction to treating dissociation as ordinary matroid independence.
• conway-jones, lam-leung, christie, steinberger, coppersmith-steinberger, tan-zhang: short and positive vanishing sums, minimal circuits, cyclotomic arrays, and certificate methods.
• dadderio-moci, onn, anderson, edmonds: arithmetic/signed dependence, primitive integer kernel moves, and the exact matroid partition analogue.
• lovitz-petrov: splitting bounds for minimally dependent product tensors.
• poonen-rubinstein: Mann localization and recursive structure for short minimal vanishing sums.
• bzdega: coefficient bounds and jumps in ternary cyclotomic polynomials.
• hindman-strauss: central sets, idempotents, and multiplicative recurrence.
• moser-tardos: the constructive asymmetric local lemma.
• tao-notes: elementary prime-sum and Mertens estimates.
• Révész: the 2007 historical formulation of the roots-of-unity Sidon and finite quasi-independent-cover questions.

Ramsey and canonization tools

• graham-rothschild, promel-voigt, voigt, karagiannis, and graham-leeb-rothschild provide possible amplification and normalization theorems. None controls the proportional extraction constant on its own; any application must prove that side separately.

Sources checked but not held

• Canfield et al., on the asymptotic enumeration of correlation-immune Boolean functions (arXiv:0909.3321), abstract, Theorem 1.2 and Corollary 1.1: the stated real-Walsh correlation-immunity enumeration range is only of order $d/\log d$, not the order near $d/2$. Not held in the library.