Combinatorics
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-1549 Loose hypergraph triangles versus cliques: an edge-rooted component certificate
- Math-1550 Free-cut decomposition for ordered matchings versus triangles
- Math-1551 A cut-cone certificate for binary transitive hosts
- Math-1552 An explicit 94-vertex cubic-residue candidate and certificate reduction
- Math-1553 Exact block-product sampling of maximal G-parking functions
- Math-1554 Unique balance and a codegree-variance obstruction for the tetrahedron conjecture
- Math-1555 Exact recursion and local profile stability for the broken tetrahedron construction
- Math-1556 Exact deficit identity for recursive tight-cycle constructions
- Math-1557 Exact trace certificates and a regular counterexample normal form for Caccetta--Haggkvist
- Math-1558 A feedback-set bound for second neighborhoods
- Math-1559 Exact anatomy of the BCW circular construction
- Math-1560 Rainbow reachability and the multi-label core obstruction
- Math-1561 A corrected colored reduction and a Sullivan-2 counterexample normal form
- Math-1562 An arc--nonedge defect identity for Sullivan-1
- Math-1563 One-sided lifting and polarized minimal counterexamples for Sullivan-3
- Math-1564 Finite-boundary transfer for infinite second neighborhoods
- Math-1565 Local edge budgets for Thomassé's nonneighbor conjecture
- Math-1566 Frontier Hall obstructions for exact distance shells
- Math-1567 A collision budget for Eulerian second neighborhoods
- Math-1568 Cut covers and small cases of Mader's local-connectivity conjecture
- Math-1569 Local average outdegree and short directed cycles
- Math-1570 Exact feedback sets in cyclic tournament substitutions
- Math-1571 A sharp lower-bound certificate for the first open transitive tournament case
- Math-1572 Defect feedback sets and a fractional obstruction for four-order majority digraphs
- Math-1573 Sliding progression-free windows via gap words
- Math-1574 Exact quadratic-residue half-set counts and a quantitative Varnavides transfer
- Math-1575 A two-sided transfer principle for the least doubling of 3-AP-free sets
- Math-1576 Cap-set status and a sharp quadratic-graph dimension barrier
- Math-1577 An explicit local-lemma certificate and bounded high-overlap neighbourhood for van der Waerden hypergraphs
- Math-1578 A diameter-free Property B bound for arbitrary van der Waerden sets
- Math-1579 Ceiling-aware bounds and a carry-free density Hales-Jewett construction
- Math-1580 Quantitative Hales-Jewett bounds and exact binary calibration
- Math-1581 Small sumsets with no three collinear
- Math-1582 Simultaneously avoiding bounded weighted averages
- Math-1583 Square-difference sets, Paley cliques, and an exact external-defect variance identity
- Math-1584 A divisor-profile lower bound and a polynomial-height near-Sidon theorem for squares
- Math-1585 Uniform iterated-sumset growth at the first doubling threshold
- Math-1586 Compact Freiman models and relation peeling
- Math-1652 Union of Fat Objects in 3D
- Math-1663 Counting Polyominoes
- Math-1737 Sharp lower bounds for entropic subspace approximation
- Math-1738 Restricted Roth progressions and their local obstructions
- Math-1739 A root-system reduction for the spherical triangle form
- Math-1740 Popular square differences: a radix obstruction and a sharp characteristic-two no-wrap model
- Math-1741 Arithmetic removal in cyclic groups: corrected quantifiers, matching distances, and exact CRT-compatible lifts
- Math-1742 Popular-direction planarization for no-five-coplanar sumsets
- Math-1743 A variational energy core for stronger BSG
- Math-1744 Good Freiman models from polynomial coset covers
- Math-1745 Riemann-profile transference for discrete entropy monotonicity
- Math-1746 Exact structure inside a two-fold sumset