Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
An almost linear time algorithm for generalized matrix searching
SIAM Journal on Discrete Mathematics
The maximum number of unit distances in a convex n-gon
Journal of Combinatorial Theory Series A
An extremal problem on sparse 0-1 matrices
SIAM Journal on Discrete Mathematics
Davenport-Schnizel theory of matrices
Discrete Mathematics
Superlinear bounds for matrix searching problems
Journal of Algorithms
Generalized Davenport-Schinzel sequences with linear upper bound
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Unprovable combinatorial statements
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
A near-linear algorithm for the planar segment center problem
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Graph Drawings with no k Pairwise Crossing Edges
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Combinatorica
Excluded permutation matrices and the Stanley-Wilf conjecture
Journal of Combinatorial Theory Series A
On 0-1 matrices and small excluded submatrices
Journal of Combinatorial Theory Series A
Splay trees, Davenport-Schinzel sequences, and the deque conjecture
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Weak ε-nets and interval chains
Journal of the ACM (JACM)
Note: On linear forbidden submatrices
Journal of Combinatorial Theory Series A
Note: Extremal functions of forbidden double permutation matrices
Journal of Combinatorial Theory Series A
Improved bounds and new techniques for Davenport--Schinzel sequences and their generalizations
Journal of the ACM (JACM)
On nonlinear forbidden 0-1 matrices: a refutation of a Füredi-Hajnal conjecture
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Applications of forbidden 0-1 matrices to search tree and path compression-based data structures
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On nonlinear forbidden 0-1 matrices: a refutation of a Füredi-Hajnal conjecture
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Generalized Davenport-Schinzel sequences and their 0-1 matrix counterparts
Journal of Combinatorial Theory Series A
On the structure and composition of forbidden sequences, with geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
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A generalized Davenport-Schinzel sequence is one over a finite alphabet that excludes subsequences isomorphic to a fixed forbidden subsequence. The fundamental problem in this area is bounding the maximum length of such sequences. Following Klazar, we let $\mathrm{Ex}(\sigma,n)$ be the maximum length of a sequence over an $n$-letter alphabet excluding subsequences isomorphic to $\sigma$. It has been proved that for every $\sigma$, $\mathrm{Ex}(\sigma,n)$ is either linear or very close to linear. In particular it is $O(n2^{\alpha(n)^{O(1)}})$, where $\alpha$ is the inverse-Ackermann function and $O(1)$ depends on $\sigma$. In much the same way that the complete graphs $K_5$ and $K_{3,3}$ represent the minimal causes of nonplanarity, there must exist a set $\Phi_{Nonlin}$ of minimal nonlinear forbidden subsequences. Very little is known about the size or membership of $\Phi_{Nonlin}$. In this paper we construct an infinite antichain of nonlinear forbidden subsequences which, we argue, strongly supports the conjecture that $\Phi_{Nonlin}$ is itself infinite. Perhaps the most novel contribution of this paper is a succinct, humanly readable code for expressing the structure of forbidden subsequences.