Tag · 3 problems · 2 fields

Open problems tagged enumeration

3 problems in the Math Lab index touch enumeration, spanning Combinatorics, Algorithms & Simulation. Each carries a precise statement, an honest status, and a computational line of attack.

Dedekind numbersCombinatoricsuntouched

D(n) counts the antichains of subsets of an n-element set — equivalently, monotone Boolean functions on n variables. Compute the next value.

Map folding & polyomino foldingAlgorithms & Simulationuntouched

Count the ways an n×m map can be folded flat along its creases — no closed form or polynomial algorithm is known even for 2×n — and decide which polyomino crease patterns fold into given 3D shapes.

Self-avoiding walksAlgorithms & Simulationuntouched

Count self-avoiding walks of length n on a lattice and pin down the connective constant μ and critical exponents. On Z² the constant is unknown (≈ 2.638).