Iterative properties of birational rowmotion. II: Rectangles and triangles.

zbMath1339.06001arXiv1402.6178MaRDI QIDQ888599

Tom Roby, Darij Grinberg

Publication date: 2 November 2015

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

Full work available at URL: https://arxiv.org/abs/1402.6178

zbMATH Keywords

graded posetsGrassmanniansroot systemsfinite posetsorder idealstropicalizationpromotionrowmotionZamolodchikov periodicity

Mathematics Subject Classification ID

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

Related Items (29)

A birational lifting of the Stanley-Thomas word on products of two chains ⋮ $P$-strict promotion and $B$-bounded rowmotion, with applications to tableaux of many flavors ⋮ The birational Lalanne-Kreweras involution ⋮ Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass ⋮ A formula for birational rowmotion on rectangles ⋮ The CDE property for minuscule lattices ⋮ 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 ⋮ \(P\)-strict promotion and piecewise-linear rowmotion, with applications to flagged tableaux ⋮ 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 ⋮ Minuscule reverse plane partitions via quiver representations ⋮ Flexible toggles and symmetric invertible asynchronous elementary cellular automata ⋮ Combinatorial, piecewise-linear, and birational homomesy for products of two chains ⋮ Moment curves and cyclic symmetry for positive Grassmannians ⋮ The CDE property for skew vexillary permutations ⋮ Affine type \(A\) geometric crystal on the Grassmannian ⋮ Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion ⋮ Iterative properties of birational rowmotion. I: Generalities and skeletal posets.

Cites Work

• Iterative properties of birational rowmotion. I: Generalities and skeletal posets.
• Promotion and rowmotion
• Iterative properties of birational rowmotion. II: Rectangles and triangles.
• Cyclic sieving, promotion, and representation theory
• On orbits of antichains of positive roots
• Two poset polytopes
• Trapezoidal chains and antichains
• 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
• An explicit bijection between semistandard tableaux and non-elliptic \(sl _{3}\) webs
• On the periodicity conjecture for \(Y\)-systems
• Homomesy in products of two chains
• A uniform bijection between nonnesting and noncrossing partitions
• Schubert Calculus
• Piecewise-linear and birational toggling
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