New perspectives on promotion and rowmotion: Generalizations and translations

Description

ABSTRACT ACKNOWLEDGEMENTS LIST OF FIGURES Introduction Semistandard Young tableaux and Gelfand–Tsetlin patterns A series of papers Promotion and rowmotion Resonance in orbits of plane partitions and increasing tableaux Rowmotion and increasing labeling promotion Piecewise-linear toggles and Q-partitions P-STRICT PROMOTION AND B-BOUNDED ROWMOTION Introduction An example Promotion on P-strict labelings Rowmotion on Q-partitions Summary of main results P-strict promotion and rowmotion Preliminary definitions First main theorem: P-strict promotion and toggle-promotion Second main theorem: P-strict promotion and rowmotion Special cases of AB"0362B((P,)) P-strict promotion and evacuation Third main theorem: P-strict promotion via jeu de taquin TEXT-strict evacuation Applications of the main theorems to tableaux of many flavors Semistandard tableaux Flagged tableaux Symplectic tableaux THE GRADED CASE Introduction Background and general results Promotion on P-strict labelings Rowmotion on Q-partitions P-strict promotion and (P,R) rowmotion The graded case: P-strict promotion and P[q-n-1] rowmotion Products of chains and multifold symmetry Application of main result to P=[a][b] Multifold symmetry Beyond the product of chains Minuscule posets Flagged product of two chains The V poset Resonance on TEXT-strict labelings Other Results and Conjectures A bijection on tableaux Order ideals of P [n] Order ideals of Raney posets Future work REFERENCES