continueing on partitions

permutation.cc

@@ -746,7 +746,7 @@ PERM_RANK_TYPE r=factorial(n);
 for(int i=1; i<=n; ++i) 
 	{
 	T m=(*this)[i];
-	if(i>1 && m>0) r/=ipow(i,m);
+	if(i>1 && m>0) r/=longpow(i,m);
 	if(m>1) r/=factorial(m);
 	}
 return r;
@@ -770,6 +770,33 @@ return factorial(n)/prod;
 }
 
 
+/*hammermesh eq 10-25, highest weight == generalized partition of r into n parts*/
+template <typename T>
+PERM_RANK_TYPE Partition<T>::Un_irrep_dim(const int n) const
+{
+#ifdef DEBUG
+if(!this->is_valid()) laerror("operation with an invalid partition");
+#endif
+std::cout<<"TEST "<<nparts()<<" "<<n<<std::endl;
+if(nparts()>n) return 0; //too antisymmetric partition
+int i,j;
+double prod;
+int r=this->size();
+NRVec_from1<int> p(n);
+for(i=1;i<=n;i++) p[i]= (i<=r?(*this)[i]:0)+n-i;
+std::cout<<"TEST "<<p<<std::endl;
+prod=1;
+for(j=n;j>=2;j--)
+        {
+        for(i=1;i<j;i++) prod*= (p[i]-p[j]);
+	prod /= factorial(j-1); //can be fractional in the intermediate steps - needs double
+	}
+
+return (PERM_RANK_TYPE) (prod+0.2);
+}
+
+
+
 template <typename T>
 Partition<T> Partition<T>::adjoint() const
 {
@@ -802,7 +829,7 @@ this->clear();
 for(int i=1; i<=nparts; ++i) (*this)[i]=x[i].size();
 }
 
-PERM_RANK_TYPE ipow(PERM_RANK_TYPE x, int i)
+PERM_RANK_TYPE longpow(PERM_RANK_TYPE x, int i)
 {
 if(i<0) return 0;
 PERM_RANK_TYPE y=1;

permutation.h

@@ -65,7 +65,7 @@ public:
 };
 
 extern PERM_RANK_TYPE factorial(const int n);
-extern PERM_RANK_TYPE ipow(PERM_RANK_TYPE x, int i);
+extern PERM_RANK_TYPE longpow(PERM_RANK_TYPE x, int i);
 
 //permutations represented in the cycle format
 template <typename T>
@@ -156,6 +156,7 @@ public:
 	explicit Partition(const YoungTableaux<T> &x); //extract a partition  as a shape of Young tableaux
 	Partition adjoint() const; //also called conjugate partition
 	PERM_RANK_TYPE Sn_irrep_dim() const;
+	PERM_RANK_TYPE Un_irrep_dim(const int n) const;
 	PERM_RANK_TYPE generate_all(void (*callback)(const Partition<T>&), int nparts=0); //nparts <0 means at most to -nparts
 
 
@@ -172,7 +173,6 @@ public:
 	int nrows() const {return this->size();}
 	int ncols() const {return (*this)[1].size();}
         bool is_standard() const; //is it filled in standard way (possibly with repeated numbers)
-	//@@@???void clear(); //clear the numbers but keep shape (different than inherited clear())
 	int sum() const; //get back sum of the partition
 	NRVec_from1<T> yamanouchi() const; //@@@yamanouchi symbol
 		//@@@ ??>young operator as a linear comb of permutations - maybe a class for itself, i.e. element of the Sn group algebra? or maybe as a vector with index being the rank of the permutation(n! length) or as a sparsemat thereof or maybe a list???
@@ -188,7 +188,6 @@ extern PERM_RANK_TYPE partitions(int n, int k= -1); //enumerate partitions to k
 
 //@@@Sn character table computation from young - young frame filling - routine for one character of one irrep and another for generation of the whole group table (maybe class for a group table too)
 //
-//@@@@Un irrep dimensions from gelfand
 
 }//namespace
 #endif

t.cc

@@ -68,16 +68,24 @@ for(int i=0; i<4; ++i)
 	}
 }
 
+static int unitary_n;
+static PERM_RANK_TYPE space_dim;
+
 void pprintme(const Partition<int> &p)
 {
 CompressedPartition pc(p);
 cout<<'['<<pc<<"] ";
 Partition<int> q=p.adjoint();
-cout<<"IR dim "<<p.Sn_irrep_dim()<<endl;
+PERM_RANK_TYPE snd=p.Sn_irrep_dim();
+cout<<"IR dim "<<snd<<endl;
+PERM_RANK_TYPE und=p.Un_irrep_dim(unitary_n);
+cout<<"U("<<unitary_n<<") ir dim "<<und<<endl;
+space_dim += und*snd;
 CompressedPartition qc(q);
 cout <<"("<<qc<<')';
 cout<<" Class size "<<qc.Sn_class_size()<<endl;
 
+/*
 int nn=p.size();
 YoungTableaux<int> y(p);
 for(int i=1; i<=y.nrows(); ++i)
@@ -89,6 +97,7 @@ YoungTableaux<int> yy(y);
 yy.clear();
 cout<<yy;
 cout <<y;
+*/
 }
 
 
@@ -2121,11 +2130,13 @@ cout <<"generated "<<tot<<endl;
 if(1)
 {
 int n;
-cin >>n;
+cin >>n >>unitary_n;
 Partition<int> p(n);
+space_dim=0;
 int tot=p.generate_all(pprintme,0);
 cout <<"generated "<<tot<<endl;
 if(tot!=partitions(n)) laerror("internal error in partition generation or enumerations");
+if(space_dim!=longpow(unitary_n,n)) {cout<<space_dim<<" "<<ipow(unitary_n,n)<<endl;laerror("integer overflow or internal error in space dimensions");}
 }