MathDBSymmetry characterization for zig-zag classes
Symmetry characterization for zig-zag classes
A zig-zag class is a class of partially ordered patterns whose underlying poset is zig-zag. Two standard operations are complementing all labels and reversing all relations.
Symmetry characterization for zig-zag classes. If two zig-zag classes are symmetrically equivalent, then one is formed by complementing the labels of the other or by reversing all of the relations of the other, or both.
This conjecture proposes that these two operations account for every symmetry class of zig-zag classes, unlike the more general situation for partially ordered pattern classes.
Sources & referencesView supporting material
Primary source
Christian Bean, Émile Nadeau, Jay Pantone and Henning Ulfarsson, “Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding”, arXiv:2312.07716 (2023).
Additional references
3 papers in this index state this conjecture (2002–2023). The statement above is taken from the most recent of them; the others are arXiv:1302.6445, arXiv:math-ph/0202018.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
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