Any permutation of ordered n-element set [n]=:{1,..., n} may be regarded as introducing a
(possibly null) measure of disorder to that set. For example, the natural order of [7] is …

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA'14], we
introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes …

We demonstrate how by using a reinforcement learning algorithm, the deep cross-entropy
method, one can find explicit constructions and counterexamples to several open …

Hints of the study of patterns in permutations date back a century, to Volume I, Section III,
Chapter V of MacMahon's 1915 magnum opus Combinatory Analysis [126]. In that work …

Twin-width is a recently introduced graph parameter with applications in algorithmics,
combinatorics, and finite model theory. For graphs of bounded degree, finiteness of twin …

We consider the problem of comparison-sorting an n-permutation S that avoids some k-
permutation π. Chalermsook, Goswami, Kozma, Mehlhorn, and Saranurak [CGK+ 15b] …

Given a labeled graph H with vertex set {1, 2,…, n}, the ordered Ramsey number r<(H) is the
minimum N such that every two-coloring of the edges of the complete graph on {1, 2,…, N} …

arXiv:1803.06636v2 [math.CO] 31 Mar 2018 Page 1 arXiv:1803.06636v2 [math.CO] 31 Mar
2018 COMPLEXITY PROBLEMS IN ENUMERATIVE COMBINATORICS IGOR PAK⋆ Abstract …

The extremal theory of forbidden 0-1 matrices studies the asymptotic growth of the function
Ex (P, n), which is the maximum weight of a matrix A∈{0, 1} n× n whose submatrices avoid a …

The dynamic optimality conjecture is perhaps the most fundamental open question about
binary search trees (BST). It postulates the existence of an asymptotically optimal online …