Using the Mathematica package OrientedSwaps

This notebook illustrates the use of the OrientedSwaps package.

Loading the package and getting help

SetDirectory["Desktop"]; (* Set the working directory to the folder where we placed the package file OrientedSwaps.m *)

<<orientedswaps.m    (* Load the package *)

OrientedSwapsHelp[]    (* This prints out a help message *)

Verifying the identity in the case n=3

genfuns = VerifyStaircaseSYTSortingNetworksIdentity[3];

genfuns   (* Inspect the two generating functions *)

Verifying the identity in the case n=4

genfuns = VerifyStaircaseSYTSortingNetworksIdentity[4];

genfuns//Column     (* Inspect the two generating functions *)

Verifying the identity in the case n=5

genfuns = VerifyStaircaseSYTSortingNetworksIdentity[5];

A complete printout of the two generating functions in this case will take up a lot of space (they each have 24 components corresponding to the 24 permutations of order 4). Here is an example of just one of the components of the two generating functions.

{genfuns[[1]][[1]],"  ",genfuns[[1]][[2]],"  ",genfuns[[1]][[3]]}//Column