combinat::yamanouchi – Yamanouchi words

The library combinat::yamanouchi provides functions for counting, generating, and manipulating Yamanouchi words.

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Cat::CombinatorialClass

Details:

Entries

"domtype"

The MuPAD domain used to represent Yamanouchi words: DOM_LIST

isA – tests if an object is a Yamanouchi word

combinat::yamanouchi::isA(word w, <<Left>, <Right>>)

Returns TRUE if w is a Yamanouchi word. By default, w will be tested as a right Yamanouchi word.

list – lists Yamanouchi words

combinat::yamanouchi::list(partition p, <<Left>, <Right>>)

Returns the list of all Yamanouchi words on the alphabet [1,2,...,n] whose evaluation is p.

By default, this function returns right Yamanouchi words.

fromTableau – Yamanouchi words from standard Young tableaux

combinat::yamanouchi::fromTableau(standard tableau t, <<Left>, <Right>>)

Returns the Yamanouchi word corresponding to the standard Young tableaux t. By default, this function returns a right Yamanouchi word.

Example 1:

combinat::yamanouchi::isA([1, 2, 2, 1, 1])

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combinat::yamanouchi::isA([1, 2, 2, 1, 1], Left)

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There are math Yamanouchi words of evaluation p = [2, 2, 2]:

combinat::yamanouchi::list([2, 2, 1])

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Left Yamanouchi words are obtained by just reverting right ones:

combinat::yamanouchi::list([2, 2, 1], Left)

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Changes in MuPAD 3.2

New Function.