Iterative properties of birational rowmotion. I: Generalities and skeletal posets.

zbMath1338.06003MaRDI QIDQ252845

Darij Grinberg, Tom Roby

Publication date: 4 March 2016

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p33

zbMATH Keywords

graded posetstreesfinite posetsbirational rowmotionorder idealstropicalization

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Algebraic combinatorics (05E99)

Related Items (23)

A birational lifting of the Stanley-Thomas word on products of two chains ⋮ The birational Lalanne-Kreweras involution ⋮ Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass ⋮ The CDE property for minuscule lattices ⋮ Some instances of homomesy among ideals of posets ⋮ Orbits of plane partitions of exceptional Lie type ⋮ Iterative properties of birational rowmotion. II: Rectangles and triangles. ⋮ \(P\)-strict promotion and \(Q\)-partition rowmotion: the graded case ⋮ Rowmotion on rooted trees ⋮ Homomesy via toggleability statistics ⋮ Birational and noncommutative lifts of antichain toggling and rowmotion ⋮ Birational rowmotion on a rectangle over a noncommutative ring ⋮ Rowmotion on fences ⋮ Cyclic sieving for plane partitions and symmetry ⋮ Birational rowmotion and Coxeter-motion on minuscule posets ⋮ \(R\)-systems ⋮ Rowmotion and increasing labeling promotion ⋮ Paths to understanding birational rowmotion on products of two chains ⋮ Resonance in orbits of plane partitions and increasing tableaux ⋮ Flexible toggles and symmetric invertible asynchronous elementary cellular automata ⋮ The CDE property for skew vexillary permutations ⋮ Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion ⋮ Iterative properties of birational rowmotion. I: Generalities and skeletal posets.

Cites Work

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• Iterative properties of birational rowmotion. I: Generalities and skeletal posets.
• Promotion and rowmotion
• Linear extensions of finite posets and a conjecture of G. Kreweras on permutations
• Iterative properties of birational rowmotion. II: Rectangles and triangles.
• Two poset polytopes
• Dual equivalence with applications, including a conjecture of Proctor
• Orbits of antichains in ranked posets
• Orbits of antichains revisited
• Combinatorial, piecewise-linear, and birational homomesy for products of two chains
• Combinatorial Markov chains on linear extensions
• Generating linear extensions of posets by transpositions
• Homomesy in products of two chains
• Piecewise-linear and birational toggling

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