A Proof of Willcocks's Conjecture
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conjecturewillcocksproofbeenchessboardexistsformulatedgive
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We give a proof of Willcocks's Conjecture, stating that if $p - q$ and $p + q$ are relatively prime, then there exists a Hamiltonian tour of a $(p, q)$-leaper on a square chessboard of side $2(p + q)$. The conjecture was formulated by T. H. Willcocks in 1976 and has been an open problem since.
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Forward citations
Cited by 2 Pith papers
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Nonexistence of Whirling-Knight Tours at Half Coil Count for $n \equiv 4, 6 \pmod 8$
No whirling-knight tours with coil count n/2 exist for n ≡ 4 or 6 mod 8, proven via closed-form Farkas certificates showing infeasibility of a cycle-cover LP relaxation.
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Nonexistence of Whirling-Knight Tours at Half Coil Count for $n \equiv 4, 6 \pmod 8$
No whirling knight's tour with winding number n/2 exists for n ≡ 4 or 6 mod 8, proven by exhibiting closed-form Farkas certificates showing infeasibility of the corresponding cycle-cover LP.
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