KAIST Discrete Math Seminar

We prove the linearity (of the lengths) of some generalized Davenport-Schinzel sequences. Standard Davenport-Schinzel sequences of order 2 (avoiding abab) are linear, while those of order 3 (avoiding ababa) and higher can be superlinear. Our goal is to determine what pattern(s), in addition to ababa, must be forbidden to regain linearity. This work is motivated by an intriguing open problem: does the lower envelope of any set of degree 3 polynomials have linear complexity?