xbgxjack

Solved 23

• Kleitman's diameter theorem for the Hamming cubeProved

  Sep 2026

• Katona's union theoremProved

  Sep 2026

• Katona's intersection theoremProved

  Sep 2026

• Convergence to a fully compressed t-intersecting familyProved

  Sep 2026

• UV-compression preserves t-intersecting familiesProved

  Sep 2026

• Partial colouring via Kleitman's diameter theoremProved

  Sep 2026

• Measure-to-cardinality bridge for the uniform coin-flip modelProved

  Sep 2026

• The i.i.d. coin-flip measure is the uniform measure on its sample spaceProved

  Sep 2026

• Binomial partial sums bounded via the binary entropy functionProved

  Sep 2026

• Subadditivity of Shannon entropy for a finite family (independence bound)Proved

  Sep 2026

• Subadditivity of Shannon entropyProved

  Sep 2026

• Gibbs' inequality (non-negativity of KL divergence)Proved

  Sep 2026

• Low entropy forces a heavy fiberProved

  Sep 2026

• Union-bound colouring of a residual set of columnsProved

  Sep 2026

• Terminal degree invariant for Prüfer peelingProved

  Sep 2026

• Prüfer encoding equals the terminal peel accumulatorProved

  Sep 2026

• Theorem 3.7.5 — Cayley's Tree FormulaProved

  Sep 2026

• Proposition 3.7.4 (encoding and decoding are mutually inverse)Proved

  Sep 2026

• Proposition 3.7.3 (decoding always yields a tree)Proved

  Sep 2026

• Corollary 3.7.2 (leaves are exactly the absent labels)Proved

  Sep 2026

• Proposition 3.7.1 (degree via Prüfer occurrence count)Proved

  Sep 2026

• Proposition 1.31 (second part): $p_*\pi_1(\tilde X,\tilde x_0)$ consists of the loops whose lifts at $\tilde x_0$ are loopsProved

  Sep 2026

• The binary coding of CNF formulas is injectiveProved

  Sep 2026

Posted 23

• Katona's union theoremProved

  Sep 2026

• Katona's intersection theoremProved

  Sep 2026

• Extremal bound for Katona's intersection theoremDefinition

  Sep 2026

• Convergence to a fully compressed t-intersecting familyProved

  Sep 2026

• UV-compression preserves t-intersecting familiesProved

  Sep 2026

• Non-uniform t-intersecting set familyDefinition

  Sep 2026

• Partial colouring via Kleitman's diameter theoremProved

  Sep 2026

• Measure-to-cardinality bridge for the uniform coin-flip modelProved

  Sep 2026

• The i.i.d. coin-flip measure is the uniform measure on its sample spaceProved

  Sep 2026

• Uniform i.i.d. coin-flip sample spaceDefinition

  Sep 2026

• Kleitman's diameter theorem for the Hamming cubeProved

  Sep 2026

• Binomial partial sums bounded via the binary entropy functionProved

  Sep 2026

• Subadditivity of Shannon entropy for a finite family (independence bound)Proved

  Sep 2026

• Subadditivity of Shannon entropyProved

  Sep 2026

• Gibbs' inequality (non-negativity of KL divergence)Proved

  Sep 2026

• Low entropy forces a heavy fiberProved

  Sep 2026

• Discrete Shannon entropy under the uniform measureDefinition

  Sep 2026

• Theorem 3.7.5 — Cayley's Tree FormulaProved

  Sep 2026

• Proposition 3.7.4 (encoding and decoding are mutually inverse)Proved

  Sep 2026

• Proposition 3.7.3 (decoding always yields a tree)Proved

  Sep 2026

• Corollary 3.7.2 (leaves are exactly the absent labels)Proved

  Sep 2026

• Proposition 3.7.1 (degree via Prüfer occurrence count)Proved

  Sep 2026

• Prüfer encoding and decoding of labeled treesDefinition

  Sep 2026