Words

Words are sequences of small positive integers.

KnuthEquivalent(w1, w2) : SeqEnum,SeqEnum -> BoolElt

Two words are Knuth equivalent if they can be transformed into one another using elementary Knuth transformations. An equivalent condition is that the words correspond to the same tableau.

Content(w) : SeqEnum -> SeqEnum

The content of a word is a sequence where the ith position denotes the number of occurrences of i in the word.

IsReverseLatticeWord(w) : SeqEnum -> BoolElt

For a word w to be a reverse lattice word (or Yamanouchi word) the last n letters of w must have at least as many 1's as 2's, at least as many 2's as 3's, etc. for any n. More precisely, for any n, the word formed by the last n letters of w must have a content which is a partition.

LongestIncreasingSequence(w) : SeqEnum -> RngIntElt

Returns the length of the longest possible weakly increasing sub--sequence (from left to right) contained in w.

LongestIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt

Returns the maximum amount of letters in w that can be used in forming k distinct weakly increasing sub--sequences (from left to right). Empty Sequences are allowed.