The sum has an alternate representation that one encounters e.g. in the OEIS (A024167).

The genera proposed by Tucker and Tenorio are recognized as an "alternate representation" by the World Register of Marine Species.

The following species name is recognized as "alternate representations" (see full explanation below).

The following species are alternate representation:

An alternate representation of the previous example would be:

An alternate representation is a suffix array, which is considered to require less virtual memory and supports data compression such as the BWT algorithm.

That is, a view is some alternate representation of, or a presentation of, and associated with, a source document.

The graphical form is an alternate compact representation of a game using the interaction among participants.

Nassarius (Aciculina) Adams, 1853 (alternate representation of Nassarius Duméril, 1805 )

At the time, this position was particularly dangerous, creating an alternate representation of the French monarchy.