[seqfan] Re: Evaluating sequences by same terms and different indices

[Heinz, Alois]

Am 04.03.2015 um 22:55 schrieb Bob Selcoe:
> Hi Seqfans,
>
> Given two (or more) sequences, each with unique terms and where all are permutations of the other, I want to evaluate and perform operations on the different indices where the terms across sequences are exactly the same.
>
> The sequences may be finite or infinite.
>
> For example, let sequences A and B be permutations of the first eight positive even numbers:
>
> A =  8   12   14   2   10   6   16   4
> B = 10   6    14  12   4    8    2   16
>
> Let terms in A be a(m) and terms in B be b(n).
>
> Order the terms so a(m) = b(n):
>
> a(4)=2, a(8)=4, a(6)=6, a(1)=8, a(5)=10, a(2)=12, a(3)=14, a(7)=16
> b(7)=2, b(5)=4, b(2)=6, b(6)=8, b(1)=10, b(4)=12, b(3)=14, b(8)=16
>
> Now we can perform operations with m and n where a(m) = b(n), including creating new sequences.  For example, C = m-n:
>
> C = -3  3  4  -5  4  -2  0  -1
>
> Alternatively, we could use the actual order of one sequence as a base, and compare the other sequence accordingly:
>
> a(1)=8, a(2)=12, a(3)=14, a(4)=2, a(5)=10, a(6)=6, a(7)=16, a(8)=4
> b(6)=8, b(4)=12, b(3)=14, b(7)=2, b(1)=10, b(2)=6, b(8)=16, b(5)=4
>
> C = -5  -2  0  -3  4  4  -1  3
>
> Of course, we could do various other operations and evaluate multiple sequences simultaneously.  I suppose we could even eliminate the requirement that the terms be unique, and make indexing rules for the repeated terms.
>
> Is there a standard name for comparing and evaluating indices of multiple sequences in this way?  Are there any OEIS sequences which use this approach??
>
> Best,
> Bob Selcoe
>              
>
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