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I'm solving some problem which is related to permutations and differences between adjacent elements in them.

For permutation (1, 2, 3, 4) the differences I'm talking about would be (+1, +1, +1)

For permutation (2, 3, 4, 1) the differences are (+1, +1, -3).

Basically it's an array ($a_1$-$a_o$, $a_2$-$a_1$, ..., $a_n$-$a_{n-1}$)

Is there a proper name for this type of mathematical object?

My English is not very good (especially when it comes to math).

Thank you

Val Petruchek
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1 Answers1

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You are talking about taking differences of the sequence. This operator on sequences is typically denoted by $\Delta$ and applied to a sequence $a_0, a_1, \ldots$ yields $$ \Delta\left((a_n)_{n=0}^\infty\right) = \left(a_n - a_{n-1}\right)_{n=1}^\infty $$

Some related discussion can be found on the Wiki entry for finite difference on the bottom.

gt6989b
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