Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify the posets for which equality holds.Comment: 13 pages, 1 figure; v2: corrected typos; v3: corrected typos and improved formatting; v4: to appear in Order; v5: corrected typos; v6: updated author email addresse

On social class, anno 2014

This article responds to the critical reception of the arguments made about social class in Savage et al. (2013). It emphasises the need to disentangle different strands of debate so as not to conflate four separate issues: (a) the value of the seven class model proposed; (b) the potential of the large web survey – the Great British Class Survey (GBCS) for future research; (c) the value of Bourdieusian perspectives for re-energising class analysis; and (d) the academic and public reception to the GBCS itself. We argue that, in order to do justice to the full potential of the GBCS, we need a concept of class which does not reduce it to a technical measure of a single variable and which recognises how multiple axes of inequality can crystallise as social classes. Whilst recognising the limitations of what we are able to claim on the basis of the GBCS, we argue that the seven classes defined in Savage et al. (2013) have sociological resonance in pointing to the need to move away from a focus on class boundaries at the middle reaches of the class structure towards an analysis of the power of elite formation

Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

Subject Benchmark Statement: Forensic Science 2012

QAA subject benchmark statement for Forensic Scienc

Social mobility at the top: how elites in the UK are pulling away

The link between geographic mobility and the reproduction of social class advantage is having a powerful effect in British society, write Katharina Hecht, Daniel McArthur, Mike Savage, and Sam Friedman. Based on an original study of changing social and geographical mobility into elite occupations, they explain why the tensions between London and the English and Welsh 'provinces' have deep roots

The Exceptions and the Rules in Global Musical Diversity

Global music diversity is a popular topic for both scientific and humanities researchers, but often for different reasons. Scientific research typically focuses on the generalities through measurement and statistics, while humanists typically emphasize exceptions using qualitative approaches. But these two approaches need not be mutually exclusive. Using a quantitative approach to identify musical outliers and a qualitative discussion of the most unusual songs, we can combine scientific and humanities approaches to unite knowledge on musical diversity. Objectively defining unusual music is a delicate task, having historically been subject to Eurocentric approaches. Using the Global Jukebox, a dataset containing almost 6,000 songs from over 1,000 societies coded on 37 “Cantometric” variables of musical style, we designate the unusualness of a song as the frequency of its coded variables relative to their regional frequency. Using quantitative metrics to identify outliers in musical diversity, we present a qualitative discussion of some of the most unusual individual songs (from a Panpipe ensemble from Kursk, Russia), and a comparison of unusual repertoires from Malay, Kel Aïr, and Moroccan Berber musical cultures. We also ask whether unusual music is the result of unusual social organisation or isolation from other groups. There is weak evidence that the unusualness of music is predicted by kinship organisation and cultural isolation, but these predictors are heavily outweighed by the finding that unusual songs are best predicted by knowing the society they come from – evidence that quantitatively supports the existence of musical style

Global musical diversity is largely independent of linguistic and genetic histories

Music is a universal yet diverse cultural trait transmitted between generations. The extent to which global musical diversity traces cultural and demographic history, however, is unresolved. Using a global musical dataset of 5242 songs from 719 societies, we identify five axes of musical diversity and show that music contains geographical and historical structures analogous to linguistic and genetic diversity. After creating a matched dataset of musical, genetic, and linguistic data spanning 121 societies containing 981 songs, 1296 individual genetic profiles, and 121 languages, we show that global musical similarities are only weakly and inconsistently related to linguistic or genetic histories, with some regional exceptions such as within Southeast Asia and sub-Saharan Africa. Our results suggest that global musical traditions are largely distinct from some non-musical aspects of human history