- Introduction
- Partitions
- Words
- Ordered Monoids
- OrderedMonoid(n) : RngIntElt -> MonOrd
- OrderedIntegerMonoid() : -> MonOrd
- Id(O) : MonOrd -> MonOrdElt
- O . i : MonOrd, RngIntElt -> MonOrdElt
- O ! [w1, ..., wn] : MonOrd, [MonOrdElt] -> MonOrdElt
- O ! [i1, ..., in] : MonOrd, [RngIntElt] -> MonOrdElt
- w1 eq w2 : MonOrdElt, MonOrdElt -> BoolElt
- w1 * w2 : MonOrdElt, MonOrdElt -> MonOrdElt
- IsKnuthEquivalent(w1, w2) : MonOrdElt, MonOrdElt -> BoolElt
- w[i] : MonOrdElt, RngIntElt -> RngElt
- ElementToSequence(w) : MonOrdElt -> SeqEnum
- Length(w) : MonOrdElt -> RngIntElt
- Content(w) : MonOrdElt -> SeqEnum[RngIntElt]
- IsReverseLatticeWord(w) : MonOrdElt -> BoolElt
- MaximalIncreasingSequence(w) : MonOrdElt -> RngIntElt
- MaximalIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt
- Example Tableau_OrderedMonoid-Creation (H154E3)
- Example Tableau_orderedmon--fingen (H154E4)
- Example Tableau_OrderedMonoid-longest (H154E5)
- Plactic Monoids
- PlacticMonoid(O) : MonOrd -> MonOrd
- PlacticIntegerMonoid() : -> MonOrd
- OrderedMonoid(P) : MonPlc -> MonOrd
- Id(P) : MonPlc -> MonPlcElt
- P . i : MonPlc, RngIntElt -> MonPlcElt
- P ! [u1, ..., un] : MonPlc, [MonPlcElt] -> MonPlcElt
- P ! [i1, ..., in] : MonPlc, [RngIntElt] -> MonPlcElt
- P ! w : MonPlc, MonOrdElt -> MonPlcElt
- P ! [w1, ..., wn] : MonPlc, [MonOrdElt] -> MonPlcElt
- P ! t : MonPlc, Tbl -> MonPlcElt
- u1 eq u2 : MonPlcElt, MonPlcElt -> BoolElt
- u1 * u2 : MonPlcElt, MonPlcElt -> MonPlcElt
- Length(u) : MonPlcElt -> RngIntElt
- Content(u) : MonPlcElt -> SeqEnum[RngIntElt]
- Example Tableau_OrderedMonoid-basic (H154E6)
- Example Tableau_OrderedMonoid-fingen (H154E7)
- Tableaux
- Tableau Monoids
- Creation of Tableaux
- Tableau(Q) : SeqEnum[RngIntElt/2] -> Tbl
- Tableau(Q) : SeqEnum[MonOrdElt] -> Tbl
- Tableau(S, Q) : SeqEnum[RngIntElt], SeqEnum[RngIntElt/2] -> Tbl
- Tableau(S, Q) : SeqEnum[RngIntElt], SeqEnum[MonOrdElt] -> Tbl
- WordToTableau(w) : MonOrdElt -> Tbl
- M ! w : MonTbl, MonOrdElt -> Tbl
- M ! u : MonTbl, MonPlcElt -> Tbl
- M ! [i1, ..., in] : MonPlc, [MonPlcElt] -> MonPlcElt
- M ! Q : MonPlc, SeqEnum -> MonPlcElt
- M ! Q : MonPlc, SeqEnum -> MonPlcElt
- Example Tableau_Tabcreate-basic (H154E10)
- Example Tableau_Tabcreate-fingen (H154E11)
- Example Tableau_Tabcreate-bang (H154E12)
- Enumeration of Tableaux
- Random Tableaux
- Basic Access Functions
- Shape(t) : Tbl -> SeqEnum[RngIntElt]
- SkewShape(t) : Tbl -> SeqEnum[RngIntElt]
- PartitionCovers(P1, P2) : SeqEnum, SeqEnum -> BoolElt
- ConjugatePartition(P) : SeqEnum -> SeqEnum
- Weight(t) : Tbl -> RngIntElt
- SkewWeight(t) : Tbl -> RngIntElt
- NumberOfRows(t) : Tbl -> RngIntElt
- NumberOfSkewRows(t) : Tbl -> RngIntElt
- Row(t, i) : Tbl, RngIntElt -> MonOrdElt
- Rows(t) : Tbl -> SeqEnum[MonOrdElt]
- Column(t, j) : Tbl, RngIntElt -> MonOrdElt
- Columns(t) : Tbl -> SeqEnum[MonOrdElt]
- RowSkewLength(t, i) : Tbl,RngIntElt -> RngIntElt
- ColumnSkewLength(t, j) : Tbl,RngIntElt -> RngIntElt
- FirstIndexOfRow(t, i) : Tbl,RngIntElt -> RngIntElt
- LastIndexOfRow(t, i) : Tbl,RngIntElt -> RngIntElt
- FirstIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
- LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
- Example Tableau_Tab-Access (H154E16)
- Properties
- Operations
- t1 eq t2 : MonPlcElt, MonPlcElt -> BoolElt
- t1 * t2 : Tbl, Tbl -> Tbl
- DiagonalSum(t1, t2) : Tbl,Tbl -> Tbl
- Conjugate(t) : Tbl -> Tbl
- JeuDeTaquin(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
- JeuDeTaquin(~t) : Tbl ->
- InverseJeuDeTaquin(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
- RowInsert(~t, w) : Tbl, MonOrdElt ->
- RowInsert(~t, x) : Tbl, RngIntElt ->
- InverseRowInsert(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
- Example Tableau_Tab-Jeu (H154E19)
- Example Tableau_Tab-Comp-Mult (H154E20)
- The Robinson-Schensted-Knuth Correspondence
- LexicographicalOrdering(~w1, ~w2) : MonOrdElt, MonOrdElt ->
- IsLexicographicallyOrdered(w1, w2) : MonOrdElt, MonOrdElt -> boolean
- RSKCorrespondence(w) : SeqEnum[RngIntElt] -> Tbl, Tbl
- InverseRSKCorrespondenceSingleWord(t1, t2) : Tbl, Tbl -> MonOrdElt
- RSKCorrespondence(w1, w2) : SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> Tbl,Tbl
- InverseRSKCorrespondenceDoubleWord(t1, t2) : Tbl, Tbl -> MonOrdElt, MonOrdElt
- RSKCorrespondence(M) : Mtrx -> Tbl, Tbl
- InverseRSKCorrespondenceMatrix(t1, t2) : Tbl, Tbl -> Mat
- Example Tableau_RSK-singleword (H154E21)
- Example Tableau_RSK-doubleword (H154E22)
- Example Tableau_RSK-Matrix (H154E23)
- Example Tableau_RSK-perms (H154E24)
- Counting Tableaux
- Bibliography
V2.28, 13 July 2023