On curves covered by the Hermitian curve

For each proper divisor d of (r^2-r+1), r being a power of a prime, maximal curves over a finite field with r^2 elements covered by the Hermitian curve of genus 1/2((r^2-r+1)/d-1) are constructed.Comment: 18 pages, Latex2

Graphical Frobenius representations of non-abelian groups

A group G has a Frobenius graphical representation (GFR) if there is a simple graph Γ whose full automorphism group is isomorphic to G acting on the vertices as a Frobenius group. In particular, any group G with a GFR is a Frobenius group and Γ is a Cayley graph. By very recent results of Spiga, there exists a function f such that if G is a finite Frobenius group with complement H and |G| > f(|H|) then G admits a GFR. This paper provides an infinite family of graphs that admit GFRs despite not meeting Spiga's bound. In our construction, the group G is the Higman group A(f, q0) for an infinite sequence of f and q0, having a nonabelian kernel and a complement of odd order

Classification of k-nets

A finite k-net of order n is an incidence structure consisting of k >= 3 pairwise disjoint classes of lines, each of size n, such that every point incident with two lines from distinct classes is incident with exactly one line from each of the k classes. Deleting a line class from a k-net, with k >= 4, gives a derived (k 1)-net of the same order. Finite k-nets embedded in a projective plane PG(2, K) coordinatized by a field K of characteristic 0 only exist for k = 3, 4, see Korchmaros et al. (2014). In this paper, we investigate 3-nets embedded in PG(2, K) whose line classes are in perspective position with an axis r, that is, every point on the line r incident with a line of the net is incident with exactly one line from each class. The problem of determining all such 3-nets remains open whereas we obtain a complete classification for those coordinatizable by a group. As a corollary, the (unique) 4-net of order 3 embedded in PG(2, K) turns out to be the only 4-net embedded in PG(2, K) with a derived 3-net which can be coordinatized by a group. Our results hold true in positive characteristic under the hypothesis that the order of the k-net considered is smaller than the characteristic of K. (C) 2015 Elsevier Ltd. All rights reserved

Out Online: The Experiences of Lesbian, Gay, Bisexual and Transgender Youth on the Internet

This report examines the online experiences of LGBT students in 6-12th grade. LGBT youth experience nearly three times as much bullying and harassment online as non-LGBT youth, but also find greater peer support, access to health information and opportunities to be civically engaged

Preface

This is the preface of the special volume of Discrete Mathematics dedicated to Combinatorics 2008 we curated as guest editors

Going That Extra Mile: Individuals Travel Further to Maintain Face-to-Face Contact with Highly Related Kin than with Less Related Kin

The theory of inclusive fitness has transformed our understanding of cooperation and altruism. However, the proximate psychological underpinnings of altruism are less well understood, and it has been argued that emotional closeness mediates the relationship between genetic relatedness and altruism. In this study, we use a real-life costly behaviour (travel time) to dissociate the effects of genetic relatedness from emotional closeness. Participants travelled further to see more closely related kin, as compared to more distantly related kin. For distantly related kin, the level of emotional closeness mediated this relationship - when emotional closeness was controlled for, there was no effect of genetic relatedness on travel time. However, participants were willing to travel further to visit parents, children and siblings as compared to more distantly related kin, even when emotional closeness was controlled for. This suggests that the mediating effect of emotional closeness on altruism varies with levels of genetic relatednes