Relating two Hopf algebras built from an operad

Starting from an operad, one can build a family of posets. From this family of posets, one can define an incidence Hopf algebra. By another construction, one can also build a group directly from the operad. We then consider its Hopf algebra of functions. We prove that there exists a surjective morphism from the latter Hopf algebra to the former one. This is illustrated by the case of an operad built on rooted trees, the \NAP operad, where the incidence Hopf algebra is identified with the Connes-Kreimer Hopf algebra of rooted trees.Comment: 21 pages, use graphics, 12 figures Version 2 : references added, minor changes. This version has not been corrected after submission. The final and corrected version will appear in IMRN and can be obtained from the author

Censorship challenges to books in Scottish public libraries

Censorship challenges to books in UK public libraries have received renewed attention recently. This study sought to establish the incidence of censorship challenges to books in Scottish public libraries in the years 2005-2009 and the actions taken in response to these challenges. It was found that eight local authorities in Scotland had received formal censorship challenges to books, with a total of 15 challenges throughout the country. The most common action taken in response to these challenges was for the book to be kept in stock in its original position with the rationale for this explained to the complainer, with the second most common action being taken to move the title to another section of the library. Two books were removed from the library in response to a censorship challenge. The largest numbers of challenges were made against books on the basis of sexual material

Simplicial and Cellular Trees

Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed first by Bolker, Kalai and Adin, and more recently by numerous authors, the fundamental topological properties of a tree --- namely acyclicity and connectedness --- can be generalized to arbitrary dimension as the vanishing of certain cellular homology groups. This point of view is consistent with the matroid-theoretic approach to graphs, and yields higher-dimensional analogues of classical enumerative results including Cayley's formula and the matrix-tree theorem. A subtlety of the higher-dimensional case is that enumeration must account for the possibility of torsion homology in trees, which is always trivial for graphs. Cellular trees are the starting point for further high-dimensional extensions of concepts from algebraic graph theory including the critical group, cut and flow spaces, and discrete dynamical systems such as the abelian sandpile model.Comment: 39 pages (including 5-page bibliography); 5 figures. Chapter for forthcoming IMA volume "Recent Trends in Combinatorics