[seqfan] Evaluating sequences by same terms and different indices

[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