Greene--Kleitman invariants for Sulzgruber insertion

A Generalization of the Greene-Kleitman Duality Theorem

In this paper, we describe and prove a generalization of both the classical Greene-Kleitman duality theorem for posets and the local version proved recently by Lewis-Lyu-Pylyavskyy-Sen in studying discrete solitons, using an approach more closely linked to the approach of the classical case.

Polyunsaturated Posets and Graphs and the Greene-Kleitman Theorem

A partition of a finite poset into chains places a natural upper bound on the size of a union of k antichains. A chain partition is k-saturated if this bound is achieved. Greene and Kleitman proved that, for each k, every finite poset has a simultaneously k- and k+1-saturated chain partition. West showed that the Greene-Kleitman Theorem is best-possible in a strong sense by exhibiting, for each c \ge 4, a poset with longest chain of cardinality c and no k- and l-saturated chain partition for any distinct, nonconsecutive k,l < c. We call such posets polyunsaturated. We give necessary and suffic…

Finite posets and Ferrers shapes

A survey on the Greene-Kleitman correspondence, with complete proofs, many of which are new.

通过 $A$ 型箭图表示的组合学对 RSK 的扩展推广

An extended generalization of RSK via the combinatorics of type $A$ quiver representations

本文通过揭示 $A$ 型箭图表示的组合学性质，构造了一族由对称群中 Coxeter 元参数化的双射，将整数划分 $λ$ 的任意填充映射到反向平面划分，并在特定参数选择下恢复了经典的 Robinson--Schensted--Knuth 对应。