The purpose of this applet is to demonstrate the jeu de taquin for standard Young tableaux with real entries (the display rounds to the nearest integer). The applet allows you to create a tableau, then use the controllers at the top to change the entries, and see how the tableau changes. The entries automatically adjust themselves according to the jdt rules, so that the tableau remains standard.
Add a new entry to a tableau: Click on an outside corner square of the existing tableau to highlight a square. Type the number (an integer) that you want to add to the tableau into the input box. Press the "+" button (or hit enter). A new entry will be created in that position. If necessary, the entries will rearrange themselves to form a tableau. Alternatively, you can type in a number without first highlighting a square. In this case, the number will be row-inserted into the existing tableau.
Delete an entry from a tableau: Click on the entry to highlight it, and press the "-" button. (Shortcut: Shift-right-click or Meta-Shift-click.)
Change the value of an existing entry: Use the controllers at the top, or highlight the entry and enter the new value into the input box. The entries will automatically rearrange themselves according to the jdt rules.
Toggle automatic jeu de taquin: When trying to modify a tableau, it can be a nuissance to have the entries constantly adjusting themselves according to the jdt rules. To turn this off, type the command freeze into the input box, and edit as before. The command unfreeze resumes normal functioning. By freezing/unfreezing, you can change the tableau in ways that would otherwise required deleting and adding entries.
Change the colour of an entry: Middle-click (or Alt-click) on the entry. The colour of the entries do not affect the jdt rules, but do change the behaviour of the checkboxes and the organization of the controllers. The "ranks" checkbox, if checked, shows the relative order of entries of the same colour. The coloured checkboxes toggle whether the entries of a particular colour are displayed.
It is possible to save a list of tableaux to memory for playback, using the commands below.