Zonshen Yu

Zonshen Yu

Two-way Superpatterns


Miklós Bóna, Zonshen Yu


Dr. Miklós Bóna


College of Liberal Arts and Sciences


<p>The concept of n-superpatterns, a permutation A which contains all patterns of length n, and many variations have been extensively studied. We introduce another variation, that of a two-way n-superpattern, which is a permutation A such that all patterns of length n are either contained in A or the reverse of A. We present a construction of a two-way n-superpattern using n*ceiling(n/2) – ceiling(n/2)*(ceiling(n/2)-1)/2 entries and compare our construction to the lengths of known two-way n-superpatterns for small n. We then connect this to the best known bounds for the shortest possible length of a n-superpattern, and investigate relationships between two-way n-superpatterns, n-superpatterns, and n-1-superpatterns.</p>


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