
arXiv: 2112.06843
This article introduces toric promotion as a cyclic analogue of Schützenberger’s promotion operator. Toric promotion acts on the set of labelings of a graph G G . We discuss connections between toric promotion and previously-studied notions such as toric posets and friends-and-strangers graphs. Our main theorem provides a surprisingly simple description of the orbit structure of toric promotion when G G is a forest.
Group actions on combinatorial structures, posets, toric posets, acyclic orientation, FOS: Mathematics, graph labeling, Mathematics - Combinatorics, Combinatorics (math.CO), 05E18, 05C05, Schützenberger promotion, Trees
Group actions on combinatorial structures, posets, toric posets, acyclic orientation, FOS: Mathematics, graph labeling, Mathematics - Combinatorics, Combinatorics (math.CO), 05E18, 05C05, Schützenberger promotion, Trees
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