When I learned Latin squares in college they were defined on A B C D ... There is another kind called Greco-Latin squares http://en.wikipedia.org/wiki/Greco-Latin_square which has another Latin square using α β γ ... superimposed on top of a Latin Square.
One time, Ken wondered out loud why it's called a "Greco-Latin square". I suggested that because they use Greek and Latin letters, but that it was only my guess. Ken said in an exasperated voice, "I bet you are right! That makes as much sense as the name 'lambda calculus'!" ----- Original Message ----- From: Henry Rich <[email protected]> Date: Monday, October 4, 2010 18:04 Subject: Re: [Jprogramming] Distinct Numbers in Rows and Columns To: Programming forum <[email protected]> > I was just using Roger's problem statement. If you want to > make it > independent of index origin, replace <: with (- >./@,) > > http://mathworld.wolfram.com/LatinSquare.html says a Latin > square uses > numbers 1-n. FWIW. > > Henry Rich > > On 10/4/2010 8:57 PM, Don Guinn wrote: > > I made a simple Latin square and tried your definition. > > > > z=:3 3$1 2 3 2 3 1 3 1 2 > > z > > 1 2 3 > > 2 3 1 > > 3 1 2 > > hr=:-.@(0&e.)@:(C.!.2)@(,|:)@:<:"2 > > hr z > > 1 > > hr>:z > > 0 > > > > I think that incrementing all numbers in z should still > produce a Latin > > square. > > > > > > > > > > > > > > On Mon, Oct 4, 2010 at 7:13 PM, Henry > Rich<[email protected]> wrote: > > > >> I got to > >> > >> -.@(0&e.)@:(C.!.2)@(,|:)@:<:"2 > >> > >> as the test for whether the item is a Latin square. I > have been trying > >> to find some cool test, without success. > >> > >> Henry Rich > >> > >> On 10/4/2010 7:37 PM, Roger Hui wrote: > >>> Great minds think alike, eh? (But I think you > >>> need to test your expressions ;-) Go to > >>> http://www.jsoftware.com/jwiki/Essays/KenKen > >>> and look about a third of the way down, > >>> > >>> q #~ (8$15) -:"1 (+/"1 ,. +/"2) q{0,2^i.4 > >>> > >>> The initial effort in your previous msg is also > >>> similar to my initial effort. > >>> > >>> > >>> > >>> ----- Original Message ----- > >>> From: Marshall Lochbaum<[email protected]> > >>> Date: Monday, October 4, 2010 16:28 > >>> Subject: Re: [Jprogramming] Distinct Numbers in Rows and Columns > >>> To: 'Programming forum'<[email protected]> > >>> > >>>> Here's a funny--and much faster--one: > >>>> p=.p:i.n > >>>> *./"1 (*/p) = (*/"2 ,. */"1) q{p > >>>> > >>>> Actually, I suppose it is better to do it with addition, so > >>>> p=.2^i.n > >>>> *./"1 (+/p) = (+/"2 ,. +/"1) q{p > >>>> > >>>> Marshall > >>>> > >>>> -----Original Message----- > >>>> From: [email protected] > >>>> [mailto:[email protected]] On Behalf Of > Roger Hui > >>>> Sent: Monday, October 04, 2010 6:41 PM > >>>> To: Programming forum > >>>> Subject: [Jprogramming] Distinct Numbers in Rows and Columns > >>>> > >>>> An interesting puzzle arising from the KenKen solver: > >>>> q is an array with shape (m,n,n) and (,q) e. 1+i.n . > >>>> Which items of q have 1+i.n in each row and in each column? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
