> Problem 2: How many of the !n permutations of even order n are > solutions to problem 1?
Problem 2 probably does not have an easy solution as the sequence 2 8 48 1152 34560 (for n=2 4 6 8 10) is not a subsequence in the Online Encyclopedia of Integer Sequences. http://www.research.att.com/~njas/sequences/index.html +/ (2 comb n)&-:@pairs@(A.&(i.n))"0 i.!n=: 2 2 +/ (2 comb n)&-:@pairs@(A.&(i.n))"0 i.!n=: 4 8 +/ (2 comb n)&-:@pairs@(A.&(i.n))"0 i.!n=: 6 48 ... ----- Original Message ----- From: Roger Hui <[email protected]> Date: Wednesday, November 11, 2009 11:03 Subject: Re: [Jprogramming] APWJ exercises for the reader [1 of 4] To: Programming forum <[email protected]> > Solution to Problem 1: > > magicperm=: C. @ < @ (|.@:>: , }.) @ (i.&.-:) > > magicperm 2 > 0 1 > magicperm 4 > 0 2 3 1 > magicperm 6 > 0 2 4 1 5 3 > magicperm 8 > 0 2 4 1 6 3 7 5 > > Check: > > seq =: 3 : 'y {^:(}:i.#y) i.#y' > pairs=: /:~ @ (>/"1 |."_1 ]) @ (_2 ]\ ,@seq) > NB. comb from http://www.jsoftware.com/help/dictionary/cfor.htm > > (2&comb -: pa...@magicperm)"0 }. 2*i.8 > 1 1 1 1 1 1 1 > > > > ----- Original Message ----- > From: Ian Clark <[email protected]> > Date: Wednesday, November 11, 2009 3:56 > Subject: [Jprogramming] APWJ exercises for the reader [1 of 4] > To: Programming forum <[email protected]> > > > In At Play With J Edn 1, there were 4 questions left as > > exercises for > > the reader. In Edn 2 we want to provide the answers in an Appendix. > > > > Just so I don't get them wrong, could the forum please suggest what > > the answers should be? You may have to refer to the Wiki page. > > > > I'm putting each question in a separate thread. > > > > +++++ > > In Chapter 5 Jacobi's method > > http://www.jsoftware.com/jwiki/Doc/Articles/Play113 [see midway] > > > > "Problem 1: Define a verb which takes as argument a positive even > > integer n and yields a permutation which, repeatedly applied > to a > > conforming identity permutation, produces, in successive pairs of > > items, all possible choices of 2 items from n, with no duplications. > > > > Problem 2: How many of the !n permutations of even order n are > > solutions to problem 1?" > > +++++ > > > > Ian Clark > > Subeditor, APWJ Edn 2 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
