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