A generalized Davenport-Schinzel sequence is one over a finite alphabet that contains no subsequences isomorphic to a fixed forbidden subsequence. One of the fundamental problems in this area is bounding (asymptotically) the maximum length of such sequences. Following Klazar, let Ex(σ, n) be the maximum length of a sequence over an alphabet of size n avoiding subsequences isomorphic to σ. It ha...

how to cite this article: singhal r, pandit s, saini a, singh p, dhawan n. the acrocallosal syndrome in a neonate with further widening of phenotypic expression. iran j child neurol. 2014 spring;8(2):60-64.   the presentation of the typical characteristics of the acrocallosal syndrome (acls) are hypoplasia/agenesis of corpus callosum, moderate to severe mental retardation, characteristic cranio...

We give a slight improvement of the best known lower bound for the supremum of autoconvolutions of nonnegative functions supported in a compact interval with a fixed integral. Also, by means of explicit examples we disprove a long standing natural conjecture of Schinzel and Schmidt concerning the extremal function for such autoconvolutions. 2000 Mathematics Subject Classification. Primary 42A85...

We present new, and mostly sharp, bounds on the maximum length of certain generalizations of Davenport-Schinzel sequences. Among the results are sharp bounds on order-s double DS sequences, for all s, sharp bounds on sequences avoiding catenated permutations (aka formation free sequences), and new lower bounds on sequences avoiding zig-zagging patterns.

An (n; s) Davenport{Schinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly non-contiguous) subsequence, any alternation a b a b of length s + 2 between two distinct symbols a and b. The close relationship between Davenport{Schinzel sequences and the c...