New perspectives on promotion and rowmotion: Generalizations and translations

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