Network realignment complexes over arbitrary connected graphs admit an equivariant deformation retraction onto a complete graph plus discrete space; for complete graphs, diameter bounds and Aut(X_n) ≅ S_n (n≥5) are established.
Kneser’s conjecture, chromatic number, and homotopy
4 Pith papers cite this work. Polarity classification is still indexing.
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math.CO 4years
2026 4representative citing papers
Transfer theorem converts max-degree independence bounds to average-degree bounds for hereditary uniform hypergraphs, with applications to cycle-free graphs and bounded-clique graphs.
Derives exact four-variable height expansion for Dyck paths with area and water-capacity weights and proves the length radius of G(x,1,p,q) equals the minimum positive real denominator branch, plus a (1-s)^{2/3} accumulation law on the diagonal.
f(n²,n) ≥ n + (1/√2 + o(1))√n and f(p²,p) ≤ 2p − (√(2/3) − o(1))√(p/log p) for large primes p.
citing papers explorer
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Network Realignment Complexes over General Graphs
Network realignment complexes over arbitrary connected graphs admit an equivariant deformation retraction onto a complete graph plus discrete space; for complete graphs, diameter bounds and Aut(X_n) ≅ S_n (n≥5) are established.
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Hypergraph independence bounds: from maximum degree to average degree
Transfer theorem converts max-degree independence bounds to average-degree bounds for hereditary uniform hypergraphs, with applications to cycle-free graphs and bounded-clique graphs.
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Area and water-capacity statistics for upper hulls of Dyck paths
Derives exact four-variable height expansion for Dyck paths with area and water-capacity weights and proves the length radius of G(x,1,p,q) equals the minimum positive real denominator branch, plus a (1-s)^{2/3} accumulation law on the diagonal.
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Hitting Arithmetic Progressions at the Square-Root Scale
f(n²,n) ≥ n + (1/√2 + o(1))√n and f(p²,p) ≤ 2p − (√(2/3) − o(1))√(p/log p) for large primes p.