Constants defined by an optimisation problem — the best bound in an inequality, the extremal value of a construction — whose exact value is unknown. Terence Tao and contributors keep the best known lower and upper bounds. An explicit construction that beats a bound is checked by recomputing it; new records should also be reported upstream.
Source: Crowdsourced repository of optimization constants (Terence Tao and contributors). Licence: Apache License 2.0.
C_22b = b_o is the largest constant for which one has an inequality L ≥ b_o C for all knots that admit an alternating diagram, where L is the ropelength of a knot (or link) with crossing number) C.
C_22a is the largest constant for which one has an inequality L≥ C_22aC^3/4 for all knots, where L is the ropelength of a knot (or link) with crossing number) C.
The constant C_42 is limsup_n→ inftyR_n, where R_n=minmax_1≤ k≤ n lvert Σ_1≤ i≤ nz_i^krvert, where the minimum is taken over all z_1,…,z_n∈ ℂ with max_i lvert z_irvert=1.
Let D=\z∈ℂ:lvert zrvert<1\ and let F be the class of holomorphic functions f:D→ℂ normalized by f'(0)=1. <a href="#BS2023-def-F">[BS2023-def-F]</a> For finF, let B_f denote the radius of the largest univalent disk in f(D).
For a finite non-empty set A of integers, C_3e is the least constant such that |A - A| ≤ |A + A|^C_3e for every such A; equivalently, C_3e = sup_A loglvert A-Arvert / loglvert A+Arvert. This is Problem 6.43 of [GGSWT2025].
Zaremba’s conjecture concerns denominators of rational numbers b/d∈(0,1) whose finite continued fraction expansions have all partial quotients bounded by an absolute constant.
