Create nonstandard tableaux, filter by a predicate, and print french style

FilterTableauByInterest

ClearAll["Global`"];
Quiet[Needs["Combinatorica`"]];

(********************************** Definitions. Don't change unless you know what you are doing. *)

(**
 * Map a function2 across a collection
 *)
Map2=#@@@Partition[#2,2,1]&;

(**
 * Are the elements of a list weakly decreasing (non-increasing) ordinally?
 *)
WeaklyIncreasingQ[list_]:=If[Length[list]<2,True,And@@Table[list[[i-1]]<=list[[i]],{i,2,Length[list]}]]

(**
 * Are the values of all rows of a tableau weakly increasing?
 *)
WeaklyIncreasingRows[t_]:=And @@ WeaklyIncreasingQ /@ t;

(**
 * Are the values of all columns of a tableau weakly increasing?
 *)
WeaklyIncreasingColumns[t_]:= WeaklyIncreasingRows[TransposeTableau[t]];

(**
 * Plot a tableau French style.
 *)
PlotTableau[t_]:=Grid[Reverse[t]/.i_Integer->Item[i,Frame->Blue],Alignment->Right](*French*);

(******************************************************** Program parameters. Change as appropriate.*)

(**
 * What partition are we interested in?
 *)
λ = {3,2,3};

(**
 * What makes a single tableau "interesting"? Return True if it is interesting, False if boring.
 *)
InterestedIn[tableau_]:=WeaklyIncreasingRows[tableau] && WeaklyIncreasingColumns[tableau];


(*Perform calculations and filter results by interest. Don't change unless you know what you are doing*)
ranges = Map2[Range[#1+1,#2]&,Accumulate[Prepend[λ,0]]];
permutations = Permutations[Range[1,Total[λ]]];
f = Function[p,p[[#]]&/@ranges];
allTableaux = f/@ permutations;

(*select the interesting ones *)
results = Select[allTableaux,InterestedIn];

(*Plot the results*)
PlotTableau/@results