MSC2020 · 05Bxx

Designs and configurations

Designs and configurations \{For applications of design theory, see 94C30\}

6 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

05B05Combinatorial aspects of block designs1 05B07Triple systems0 05B10Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)0 05B15Orthogonal arrays, Latin squares, Room squares0 05B20Combinatorial aspects of matrices (incidence, Hadamard, etc.)3 05B25Combinatorial aspects of finite geometries1 05B30Other designs, configurations1 05B35Combinatorial aspects of matroids and geometric lattices0 05B40Combinatorial aspects of packing and covering0 05B45Combinatorial aspects of tessellation and tiling problems0 05B50Polyominoes0 05B99Designs and configurations0

Mapped problems

OP-12132CombinatoricsStatus unassessed

Spherical Designs (AlphaEvolve problem 32)

Spherical Designs (AlphaEvolve problem 32). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12106CombinatoricsStatus unassessed

Kakeya and Nikodym sets in finite fields (AlphaEvolve problem 1)

Kakeya and Nikodym sets in finite fields (AlphaEvolve problem 1). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12031CombinatoricsOpen

Asymptotic counting exponent for partial Hadamard matrices ( $C_{23c}$ )

Asymptotic counting exponent for partial Hadamard matrices: determine C 23c or improve its bounds; the repository records 1 (lower) and 3 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12029CombinatoricsOpen

Smallest unsolved instance of the Hadamard conjecture ( $C_{23a}$ )

Smallest unsolved instance of the Hadamard conjecture: determine C 23a or improve its bounds; the repository records 668 (lower) and infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11967CombinatoricsOpen

Large Steiner Systems

Large Steiner Systems. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11960CombinatoricsSolved

Hadamard Matrix of Order 668

Hadamard Matrix of Order 668. Moderately interesting problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

Journals & articles in MSC 05

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Electronic Journal of Combinatorics ↗

Electronic Journal of Combinatorics

Combinatorics and graph theory

Journal discovery is available; article-level extraction for this class is not yet included in this batch.

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