Re: Multiplying permutations
- To: mathgroup at smc.vnet.net
- Subject: [mg41844] Re: Multiplying permutations
- From: "Carl K. Woll" <carlw at u.washington.edu>
- Date: Sat, 7 Jun 2003 00:08:35 -0400 (EDT)
- Organization: University of Washington
- References: <bbhvu4$75u$1@smc.vnet.net> <bbq8rg$d91$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Wolfgang,
Just add the attributes Flat and OneIdentity to CenterDot, as follows:
SetAttributes[CenterDot,{Flat,OneIdentity}]
p_\[CenterDot]q_:=q[[p]]
and everything should work nicely.
Carl Woll
Physics Dept
U of Washington
"Dr. Wolfgang Hintze" <weh at snafu.de> wrote in message
news:bbq8rg$d91$1 at smc.vnet.net...
> How can I define multiple products recursively?
>
> Example permutations
>
> p = {3, 1, 2};
> q = {2, 1, 3};
> r = {3, 2, 1};
>
> Carl's defintion of the product
>
> p_·q_ := q[[p]]
>
> works fine for 2 factors:
>
> In[237]:=
> p · q
>
> Out[237]=
> {3, 2, 1}
>
> Now let's try 3 factors
>
> In[240]:=
> p · q · r
>
> Out[240]=
> {3, 1, 2} · {2, 1, 3} · {2, 3, 1}
>
> Using brackets we get what we want
>
> In[265]:=
> (p · q) · r
> p · (q · r)
>
> Out[265]=
> {1, 3, 2}
>
> Out[266]=
> {1, 3, 2}
>
> Despite of the associativeness of the product we need brackets.
> Hence if we define for 3 factors
>
> In[242]:=
> p_ · q_ · r_ := (p · q) · r
>
> we can get
>
> In[278]:=
> p · q · r
>
> Out[278]=
> {1, 3, 2}
>
> But a product of 4 factors still is not defined.
> Question: How can a general recursive definition be given?
>
> Wolfgang
>
>
>
> Dr. Wolfgang Hintze wrote:
>
> > Is there a simple command in Mathematica to multiply two permutations,
> > i.e. to carry out one after the other?
> >
> > I looked at the packages DiscreteMath`Permutations` and
> > DiscreteMath`Combinatorica` but couldn't find it.
> >
> > Example
> >
> > p = {3,1,2} mapping: 1->3, 2->1, 3->2
> > q = {2,1,3} mapping: 1->2, 2->1, 3->3
> > p.q = mappings (p first, then q)
> > [1-p->3-q->3, 2-p->1-q->2, 3-p->2-q->1]
> > = {3,2,1}
> >
> > Any help appreciated
> >
> > Wolfgang
> >
> >
>