The Davenport–Schinzel sequence is a mathematical concept in combinatorial geometry that deals with sequences of symbols. It is defined by the property that no two adjacent symbols in the sequence can be the same, and it avoids certain patterns of repetition. This sequence is important in the study of geometric problems and has applications in areas like computer science and discrete mathematics. The length of a Davenport–Schinzel sequence can be bounded based on the number of symbols used and the restrictions on the patterns. Specifically, for a sequence of length n with k symbols, the maximum length can be expressed in terms of n and k , leading to insights in various fields, including algorithm design and data structures.