OFFSET
0,7
COMMENTS
I.e. the permutation on the partitions of n which maps the k-th partition in Abramowitz and Stegun order to the k-th partition in Mathematica order. - Franklin T. Adams-Watters, Jun 14 2006
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
EXAMPLE
a(7) = 6 = order of (1,2,3,5,4,6,8,9,7,10,12,11,13,14,15) = order of (4,5) (7,8,9) (11,12)
PROG
(PARI)
Dual(v)={my(u=vectorsmall(v[1]), k=0); forstep(i=#u, 1, -1, while(k<#v&&v[k+1]>=i, k++); u[i]=k); u}
OrderCycs(v)={my(t=vector(#v), L=List()); for(i=1, #v, my(c=0, j=i); while(!t[j], t[j]=1; j=v[j]; c++); if(c, listput(L, c))); Vec(L)}
a(n)={my(u=vecsort([Vecsmall(Vecrev(p)) | p<-partitions(n)])); my(v=vector(#u, i, vecsearch(u, Dual(u[#u+1-i])))); vecprod(Set(OrderCycs(v)))} \\ Andrew Howroyd, Sep 17 2019
(PARI) \\ alternate program, see above for OrderCycs.
a(n)={my(v=vecsort([Vecsmall(Vecrev(p)) | p<-partitions(n)], , 1+4)); vecprod(Set(OrderCycs(v)))} \\ Andrew Howroyd, Sep 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name changed to agree with data and a(0) = 1 prepended by Andrew Howroyd, Sep 17 2019
STATUS
approved