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 …

Analytic combinatorics aims to enable precise quantitative predictions of the properties of
large combinatorial structures. The theory has emerged over recent decades as essential …

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics
whose basic blocks are ordinal patterns, that is, permutations defined by the order relations …

This book presents a systematic treatment of Grobner bases in several contexts. The book
builds up to the theory of Grobner bases for operads due to the second author and …

We say that two sequences x and w of length m are order-isomorphic (of the same “shape”)
if w [i]⩽ w [j] if and only if x [i]⩽ x [j] for each i, j∈[1, m]. We present a simple linear time …

Contemporary biomedical research is performed by increasingly large teams. Consequently,
an increasingly large number of individuals are being listed as authors in the bylines, which …

This book is about how symmetric functions can be used in enumeration. The development
is entirely self-contained, including an extensive introduction to the ring of symmetric …

The study of order patterns of three equally-spaced values xt, xt+ d, xt+ 2 d in a time series is
a powerful tool. The lag d is changed in a wide range so that the differences of the …

We consider two problems that appear at first sight to be unrelated. The first problem is to
count certain diagrams consisting of noncrossing arcs in the plane. The second problem …

We study linear recurrences of Eulerian type of the form P n (v)=(α (v) n+ γ (v)) P n− 1 (v)+ β
(v)(1− v) P n− 1′(v)(n⩾ 1), with P 0 (v) given, where α (v), β (v) and γ (v) are in most cases …