W1W2

w1w2 is a notation used to denote the concatenation of two elements named w1 and w2. In formal language theory, if w1 and w2 are strings over an alphabet Σ, w1w2 denotes their concatenation, a new string formed by placing w2 directly after w1. The operation is associative, and the length satisfies |w1w2| = |w1| + |w2|. The set Σ* of all strings forms a monoid under concatenation, with the empty string ε as the identity.

In other contexts, w1w2 may refer to combining two word representations in natural language processing. If w1 and w2 are vectors or features, concatenating them yields a longer representation [w1; w2] used for multi-token encoding or fixed-length input. When treated as text, w1w2 can be the literal join of two words, for example w1 = "ice" and w2 = "cream" giving w1w2 = "icecream".

In programming languages, the concrete method to form w1w2 varies: some provide a string concatenation operator such as +, others allow implicit adjacency, and some offer a dedicated function. The interpretation depends on data types and the application context.

See also concatenation, vector concatenation, and word embedding.