User talk:Mike Winkler

A293308

A draft covers your sequence (17) on page 9 of arxiv.org/pdf/1709.03385. –Frank Ellermann 18:03, 5 October 2017 (UTC)

(meanwhile approved): I think one of the programs in your paper actually generates this sequence, but I wasn't sure. Maybe add it as another way to compute/check the terms. –Frank Ellermann 07:38, 13 October 2017 (UTC)

Thanks for adding this sequence. Program 6 on page 17 in my paper shows the PARI function "NextPermutation(a)". It shows one possibility for generating all permutations in lexicographic ordering of such a zero-one tuple. This special order is relevant for the context of my paper. I do not know, if this is relevant for the "number of permutations" showing in A293308.

NextPermutation(a) = {i=#a-1; while(!(i<1 || a[i]<a[i+1]), i--); if(i<1, return(0)); k=#a; while(!(a[k]>a[i]), k--); t=a[k]; a[k]=a[i]; a[i]=t; for(k=i+1, (#a+i)/2, t=a[k]; a[k]=a[#a+1+i-k]; a[#a+1+i-k]=t; ); return(a)}

Example: all permutations in lexicographic ordering of (0, 0, 1, 1, 1, 1) are given by the PARI code

{n=1; a=[0, 0, 1, 1, 1, 1]; until(a==0, print(n" "a); n++; a=NextPermutation(a))}

which outputs

1 [0, 0, 1, 1, 1, 1]
2 [0, 1, 0, 1, 1, 1]
3 [0, 1, 1, 0, 1, 1]
4 [0, 1, 1, 1, 0, 1]
5 [0, 1, 1, 1, 1, 0]
6 [1, 0, 0, 1, 1, 1]
7 [1, 0, 1, 0, 1, 1]
8 [1, 0, 1, 1, 0, 1]
9 [1, 0, 1, 1, 1, 0]
10 [1, 1, 0, 0, 1, 1]
11 [1, 1, 0, 1, 0, 1]
12 [1, 1, 0, 1, 1, 0]
13 [1, 1, 1, 0, 0, 1]
14 [1, 1, 1, 0, 1, 0]
15 [1, 1, 1, 1, 0, 0]

Thanks, A293308 looks good now. I just wondered why I have your user page in my "watch list" here, it was about this talk page. Unwatching now, otherwise I'd end up as "talk page stalker" ;-) –Frank Ellermann 15:56, 13 November 2017 (UTC)