Cyclic inclusion-exclusion

Following the lead of Stanley and Gessel, we consider a morphism which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing functions on the graph. We describe the kernel of this morphism, using a simple combinatorial operation that we call cyclic inclusion-exclusion. Our result also holds for the natural noncommutative analog and for the commutative and noncommutative restrictions to bipartite graphs. An application to the theory of Kerov character polynomials is given.Comment: comments welcom

Cyclic inclusion-exclusion and the kernel of P -partitions

International audienceFollowing the lead of Stanley and Gessel, we consider a linear map which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing functions on the graph (or of P -partitions of the poset).We describe the kernel of this linear map, using a simple combinatorial operation that we call cyclic inclusion- exclusion. Our result also holds for the natural non-commutative analog and for the commutative and non-commutative restrictions to bipartite graphs

Cyclic inclusion-exclusion and the kernel of P -partitions

Following the lead of Stanley and Gessel, we consider a linear map which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing functions on the graph (or of P -partitions of the poset).We describe the kernel of this linear map, using a simple combinatorial operation that we call cyclic inclusion- exclusion. Our result also holds for the natural non-commutative analog and for the commutative and non-commutative restrictions to bipartite graphs

Gay men, Gaydar and the commodification of difference

Purpose To investigate ICT mediated inclusion and exclusion in terms of sexuality through a study of a commercial social networking website for gay men Design/methodology/approach The paper uses an approach based on technological inscription and the commodification of difference to study Gaydar, a commercial social networking site. Findings Through the activities, events and interactions offered by Gaydar, we identify a series of contrasting identity constructions and market segmentations which are constructed through the cyclic commodification of difference. These are fuelled by a particular series of meanings attached to gay male sexualities which serve to keep gay men positioned as a niche market. Research limitations/implications The research centres on the study of one, albeit widely used, website with a very specific set of purposes. The study offers a model for future research on sexuality and ICTs. Originality/value This study places sexuality centre stage in an ICT mediated environment and provides insights into the contemporary phenomenon of social networking. As a sexualized object, Gaydar presents a semiosis of politicized messages that question heteronormativity while simultaneously contributing to the definition of an increasingly globalized, commercialized and monolithic form of gay male sexuality defined against ICT

Cyclic derangements

A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we generalize this problem to enumerating derangements in the wreath product of any finite cyclic group with the symmetric group. We also give q- and (q, t)-analogs for cyclic derangements, generalizing results of Brenti and Gessel.Comment: 14 page

Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p^n

Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p^{n+1} extension E'/F, we give a more refined F_p[Gal(E/F)]-decomposition of H^m(G_E,mu_p)

Supporting Usability and Reusability Based on eLearning Standards

The IMS-QTI, and other related specifications have been developed to support the creation of reusable and pedagogically neutral assessment scenarios and content, as stated by the IMS Global Learning Consortium. In this paper we discuss how current specifications both constrain the design of assessment scenarios, and limit content reusability. We also suggest some solutions to overcome these limitations. The paper is based on our experience developing and testing an IMS QTI Lite compliant assessment authoring tool, QAed. It supports teacher centering, which is quite neglected when designing such tools. In the paper we also discuss how to make compatible standards support and user centering in eLearning applications and provide some recommendations for the design of the user interfaces