bruijn

Bruijn is a Dutch surname, sometimes written as de Bruijn or De Bruijn. The name is of Dutch origin and appears in various family names and place-based identifiers. Spelling variations reflect typical Dutch surname conventions, including the use of the definite article de.

Notable individuals with the surname include Nicolaas Govert de Bruijn (1918–2012), a Dutch mathematician whose work spanned combinatorics, number theory, and graph theory. He is best known for introducing concepts later named after him, such as the De Bruijn graph, the De Bruijn sequence, and the De Bruijn notation in lambda calculus.

De Bruijn graph: A directed graph used in combinatorics and computer science. For a chosen alphabet and a fixed length, its vertices represent strings of a certain length, and its edges represent extensions by one symbol, connecting prefixes to suffixes. The graph often contains an Eulerian path or cycle under appropriate conditions, making it useful for problems involving overlaps, such as genome assembly, data compression, and network design.

De Bruijn sequence: A cyclic sequence over an alphabet where every possible length-n string appears exactly once as a contiguous subsequence. Existence is guaranteed for any alphabet size and length, and such sequences are utilized in coding theory, digital communications, and sequence design for testing and sampling.

De Bruijn notation: A binding representation in lambda calculus that uses numeric indices to indicate the distance to a binding lambda, avoiding variable names and alpha-conversion. This notation simplifies formal manipulation of bound variables in some theoretical and practical contexts.

The Bruijn surname thus relates to several foundational ideas in mathematics and computer science, most prominently through Nicolaas Govert de Bruijn and the associated graph, sequence, and notation concepts.