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arXiv · 1603.01736

Some Results on Superpatterns for Preferential Arrangements

Yonah Biers-Ariel·Yiguang Zhang·Anant Godbole
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Abstract

A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results on superpatterns for {\em preferential arrangements}, including (i) a theorem that demonstrates that a string is a superpattern for all preferential arrangements if and only if it is a superpattern for all permutations; and (ii) a result that is reminiscent of a still unresolved conjecture of Alon on the smallest permutation on $[n]$ that contains all $k$-permutations with high probability.

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Yonah Biers-Ariel, Yiguang Zhang, Anant Godbole. 2016-03-05. Some Results on Superpatterns for Preferential Arrangements. https://arxiv.org/abs/1603.01736

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