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arxiv: math/0009230 · v1 · submitted 2000-09-26 · 🧮 math.CO

The conjecture cr(C_mtimes C_n)=(m-2)n is true for all but finitely many n, for each m

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keywords conjectureadamssonfinitelymanyprovedtimestruearrangements
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It has been long congectured that the crossing number of $C_m\times C_n$ is $(m-2)n$ for $2<m<=n$. In this paper we proved that conjecture is true for all but finitely many $n$ for each $m$. More specifically we proved conjecture for $n>=(m/2)((m+3)^2/2+1)$.The proof is largely based on the theory of arrangements introduced by Adamsson and further developed by Adamsson and Richter.

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