Thrall's problem for two rows
The bijection ξ
For T∈SYT=(2n), construct D=(Φ0 ∘ Ω ∘ ΨU)(S) in ξ(T)=(U,D).
n ≤ 5: uniform. n > 5: random in SYT=(2n), not guaranteed uniform.
Write one row of T per line. Example: 1 2 4 7 9.
If T∉SYT=(2n), then ξ(T)
is not defined; for comparison, the construction continues with
rect(S) in place of U.