combinatorics / Permutational Ramsey theory

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

Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed nn, witnessed satisfiable at n−1n-1. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the KK column. The three overlap cells are Rdih(P4alt,K6)=16R_{dih}(P_4^{alt},K_6)=16, Rdih(P3alt,K9)=17R_{dih}(P_3^{alt},K_9)=17 and Rdih(P9alt,K3)=17R_{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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combinatoricsAug 13, 2026Significance 5/100Registry: site confirmed

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

Prior state unknown→proved

Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed nn, witnessed satisfiable at n−1n-1. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the KK column. The three overlap cells are Rdih(P4alt,K6)=16R_{dih}(P_4^{alt},K_6)=16, Rdih(P3alt,K9)=17R_{dih}(P_3^{alt},K_9)=17 and Rdih(P9alt,K3)=17R_{dih}(P_9^{alt},K_3)=17, each an instance of a sibling theorem; the remain…

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Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed nn, witnessed satisfiable at n−1n-1. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the KK column. The three overlap cells are Rdih(P4alt,K6)=16R_{dih}(P_4^{alt},K_6)=16, Rdih(P3alt,K9)=17R_{dih}(P_3^{alt},K_9)=17 and Rdih(P9alt,K3)=17R_{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.

Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed nn, witnessed satisfiable at n−1n-1. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the KK column. The three overlap cells are Rdih(P4alt,K6)=16R_{dih}(P_4^{alt},K_6)=16, Rdih(P3alt,K9)=17R_{dih}(P_3^{alt},K_9)=17 and Rdih(P9alt,K3)=17R_{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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