Marking boundaries and identities: the precolonial expansion of segmentary societies in Southwestern Burkina Faso

Over approximately the last 200 years, north-west Ghana and large areas of neighbouring southern Burkina Faso were the stage for a highly successful expansion of Dagara-speaking peoples. Probably setting out from an area around Wa, small groups of Dagara migrated towards the north, some of them taking a westward route, crossing the Black Volta river into today’s Burkina Faso. They rarely advanced into nomansland but rather displaced peoples such as Sisala-, Dyan-, Phuie- and Bwamu-speaking groups, who then moved further west and north. Today, the Dagara occupy about 3500 km2 in southern Burkina Faso, where they represent the sixth largest language group. In this paper I wish to explore the history of the north-west frontier of Dagara expansion and the interaction between the “land-owning” Phuo and the incoming Dagara

A Note on the generating function of p-Bernoulli numbers

We use analytic combinatorics to give a direct proof of the closed formula for the generating function of $p$-Bernoulli numbers.Comment: 6 page

Combinatorial families of multilabelled increasing trees and hook-length formulas

In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in the tree can get multiple labels. For all tree classes we show characterizations of suitable generating functions for the tree enumeration sequence via differential equations. Furthermore, for several combinatorial classes of multilabelled increasing tree families we present explicit enumeration results. We also present multilabelled increasing tree families of an elliptic nature, where the exponential generating function can be expressed in terms of the Weierstrass-p function or the lemniscate sine function. Furthermore, we show how to translate enumeration formulas for multilabelled increasing trees into hook-length formulas for trees and present a general "reverse engineering" method to discover hook-length formulas associated to such tree families.Comment: 37 page

On martingale tail sums in affine two-color urn models with multiple drawings

In two recent works, Kuba and Mahmoud (arXiv:1503.090691 and arXiv:1509.09053) introduced the family of two-color affine balanced Polya urn schemes with multiple drawings. We show that, in large-index urns (urn index between $1/2$ and $1$) and triangular urns, the martingale tail sum for the number of balls of a given color admits both a Gaussian central limit theorem as well as a law of the iterated logarithm. The laws of the iterated logarithm are new even in the standard model when only one ball is drawn from the urn in each step (except for the classical Polya urn model). Finally, we prove that the martingale limits exhibit densities (bounded under suitable assumptions) and exponentially decaying tails. Applications are given in the context of node degrees in random linear recursive trees and random circuits.Comment: 17 page