Simply generated families of trees are described by the equation T (z) = φ(T (z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ {1, . . . , n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are ...

The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoid...

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel 1/(1 − θx) in place of the celebrated exponential kernel exp(θx) of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-i...

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generat...

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generat...

We develop the geometry of the Cayley graph of the lamplighter group with respect to the generating set rising from its interpretation as an automata group [4]. We find metric behavior with respect to this generating set analogous to the metric behavior in the standard group theoretic generating set. This includes expressions for normal forms and geodesic paths, and families of ‘dead-end’ words...

The paper investigates the strategic behavior of hedge fund families. It focuses on decisions to start and liquidate family-member funds. Hedge fund families tend to liquidate funds that underperform compared to other member funds, and to replace them by new ones. By choosing a launch time after a short period of superior performance by their member funds, families extend the spillover to new f...