combinatorics / Permutational Ramsey theory

Nineteen exact reflective and dihedral Ramsey numbers from Damnjanovic-Dordevic's tables

Sixteen previously unknown exact values, plus three that confirm the sibling theorem entries' predictions computationally, across five ordered-pattern families ($P^{alt}$, $S^{sc}$, $C^{mon}$, $M^{nest}$, $K$) under dihedral and reflective group actions - each closing one open cell of Damnjanovic-Dordevic (arXiv:2607.06817, Tables 3-13). Five sit in cells the paper left without a conjecture. Full per-value table with regeneration commands, certificate hashes and referee verdicts in the evidence repo.

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combinatoricsAug 13, 2026Significance 5/100Registry: site confirmed

Nineteen exact reflective and dihedral Ramsey numbers from Damnjanovic-Dordevic's tables

Prior state unknownproved

Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed $n$, witnessed satisfiable at $n-1$. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the $K$ column. The three overlap cells are $R_{dih}(P_4^{alt},K_6)=16$, $R_{dih}(P_3^{alt},K_9)=17$ and $R_{dih}(P_9^{alt},K_3)=17$, each an instance of a sibling theorem; the rema…

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Sixteen previously unknown exact values, plus three that confirm the sibling theorem entries' predictions computationally, across five ordered-pattern families ($P^{alt}$, $S^{sc}$, $C^{mon}$, $M^{nest}$, $K$) under dihedral and reflective group actions - each closing one open cell of Damnjanovic-Dordevic (arXiv:2607.06817, Tables 3-13). Five sit in cells the paper left without a conjecture. Full per-value table with regeneration commands, certificate hashes and referee verdicts in the evidence repo.

Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed $n$, witnessed satisfiable at $n-1$. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the $K$ column. The three overlap cells are $R_{dih}(P_4^{alt},K_6)=16$, $R_{dih}(P_3^{alt},K_9)=17$ and $R_{dih}(P_9^{alt},K_3)=17$, each an instance of a sibling theorem; the remaining sixteen stand on their own certificates. Four further cells passed the producing solver but await their final referee leg and are not claimed. Open: every other cell of DD26's tables, all cyclic-action and online-Ramsey cells.

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