A differential poset is a locally finite graded partially ordered set with a unique minimum, finite ranks, and up and down cover operators satisfying for a fixed positive integer . The Young lattice has : distinct equal-rank diagrams have equally many common upper and lower covers, and each diagram has one more upper cover than lower cover.
If , commuting every past every gives . The recurrence follows from . Applied to the empty diagram in the Young lattice, it counts oscillating tableaux.
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A **differential poset** (short for "differential partially ordered set") is a concept used in the study of combinatorics and order theory. While the term itself is not universally defined across all areas of mathematics, it generally refers to a partially ordered set (poset) that has some structure or properties related to differential operations, which might be in the context of algebraic structures or certain combinatorial interpretations.