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arXiv · 1808.04199

Passing through a stack $k$ times with reversals

Toufik Mansour·Howard Skogman·Rebecca Smith
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Abstract

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass sortable permutations and give computational results for some classes with larger maximal rev-tier. We also show all classes of $(t+1)$-reverse pass sortable permutations are finitely based. Additionally, a new Entringer family consisting of maximal rev-tier permutations of length $n$ was discovered along with a bijection between this family and the collection of alternating permutations of length $n-1$. We calculate generating functions for the number permutations of length $n$ and exact rev-tier $t$.

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Toufik Mansour, Howard Skogman, Rebecca Smith. 2018-08-13. Passing through a stack $k$ times with reversals. https://arxiv.org/abs/1808.04199

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