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| author | dos-reis <gdr@axiomatics.org> | 2010-04-22 01:40:53 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-04-22 01:40:53 +0000 |
| commit | 9fac9abefef7f727a59b7861317d148352a43d88 (patch) | |
| tree | 6cf281301d4609d71aae0540b6cd098abd41de2b /src/algebra/sgcf.spad.pamphlet | |
| parent | dca6da4bba9a14e544345d4b54f623450d47f283 (diff) | |
| download | open-axiom-9fac9abefef7f727a59b7861317d148352a43d88.tar.gz | |
* algebra/irsn.spad.pamphlet (IrrRepSymNatPackage): Tidy.
* algebra/partperm.spad.pamphlet (PartitionsAndPermutations): Likewise.
* algebra/cycles.spad.pamphlet (complete$CycleIndicators): Now
take only positive integers.
(powerSum$CycleIndicators): Likewise.
(elementary$CycleIndicators): Likewise.
(alternating$CycleIndicators): Likewise.
(cyclic$CycleIndicators): Likewise.
(dihedral$CycleIndicators): Likewise.
(graphs$CycleIndicators): Likewise.
Diffstat (limited to 'src/algebra/sgcf.spad.pamphlet')
| -rw-r--r-- | src/algebra/sgcf.spad.pamphlet | 19 |
1 files changed, 10 insertions, 9 deletions
diff --git a/src/algebra/sgcf.spad.pamphlet b/src/algebra/sgcf.spad.pamphlet index 5f1dfa6b..72669658 100644 --- a/src/algebra/sgcf.spad.pamphlet +++ b/src/algebra/sgcf.spad.pamphlet @@ -48,6 +48,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where V ==> Vector B ==> Boolean ICF ==> IntegerCombinatoricFunctions Integer + macro PI == PositiveInteger public ==> with @@ -85,7 +86,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where ++ is given in list form. ++ Notes: the inverse of this map is {\em coleman}. ++ For details, see James/Kerber. - listYoungTableaus : (L I) -> L M I + listYoungTableaus : L PI -> L M I ++ listYoungTableaus(lambda) where {\em lambda} is a proper partition ++ generates the list of all standard tableaus of shape {\em lambda} ++ by means of lattice permutations. The numbers of the lattice @@ -95,7 +96,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where ++ Notes: the functions {\em nextLatticePermutation} and ++ {\em makeYoungTableau} are used. ++ The entries are from {\em 0,...,n-1}. - makeYoungTableau : (L I,L I) -> M I + makeYoungTableau : (L PI,L I) -> M I ++ makeYoungTableau(lambda,gitter) computes for a given lattice ++ permutation {\em gitter} and for an improper partition {\em lambda} ++ the corresponding standard tableau of shape {\em lambda}. @@ -107,7 +108,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where ++ to the lexicographical order from bottom-to-top. ++ The first Coleman matrix is achieved by {\em C=new(1,1,0)}. ++ Also, {\em new(1,1,0)} indicates that C is the last Coleman matrix. - nextLatticePermutation : (L I, L I, B) -> L I + nextLatticePermutation : (L PI, L I, B) -> L I ++ nextLatticePermutation(lambda,lattP,constructNotFirst) generates ++ the lattice permutation according to the proper partition ++ {\em lambda} succeeding the lattice permutation {\em lattP} in @@ -280,9 +281,9 @@ SymmetricGroupCombinatoricFunctions(): public == private where nextLatticePermutation(lambda, lattP, constructNotFirst) == - lprime : L I := conjugate(lambda)$PartitionsAndPermutations - columns : NNI := (first(lambda)$(L I))::NNI - rows : NNI := (first(lprime)$(L I))::NNI + lprime := conjugate(lambda)$PartitionsAndPermutations + columns := first(lambda)$L(PI) + rows := first(lprime)$L(PI) n : NNI :=(+/lambda)::NNI not constructNotFirst => -- first lattice permutation @@ -332,9 +333,9 @@ SymmetricGroupCombinatoricFunctions(): public == private where makeYoungTableau(lambda,gitter) == - lprime : L I := conjugate(lambda)$PartitionsAndPermutations - columns : NNI := (first(lambda)$(L I))::NNI - rows : NNI := (first(lprime)$(L I))::NNI + lprime := conjugate(lambda)$PartitionsAndPermutations + columns := first(lambda)$L(PI) + rows := first(lprime)$L(PI) ytab : M I := new(rows,columns,0) help : V I := new(columns,1) i : I := -1 -- this makes the entries ranging from 0,..,n-1 |