Using the Dantzig's pivoting rule, can it be proven that the leaving variable of one round cannot be selected as the entering variable in the next round?

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    $\begingroup$ If we talk primal simplex then I think you can prove that the reduced cost of the outgoing variable is such such it will not be a candidate. Outgoing reduced cost is something like incoming reduced cost divided by pivot element. $\endgroup$ – ErlingMOSEK May 20 '20 at 5:09

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