An explicit universal cycle for the (n-1)-permutations of an n-set

We show how to construct an explicit Hamilton cycle in the directed Cayley graph Cay({\sigma_n, sigma_{n-1}} : \mathbb{S}_n), where \sigma_k = (1 2 >... k). The existence of such cycles was shown by Jackson (Discrete Mathematics, 149 (1996) 123-129) but the proof only shows that a certain directed graph is Eulerian, and Knuth (Volume 4 Fascicle 2, Generating All Tuples and Permutations (2005)) asks for an explicit construction. We show that a simple recursion describes our Hamilton cycle and that the cycle can be generated by an iterative algorithm that uses O(n) space. Moreover, the algorithm produces each successive edge of the cycle in constant time; such algorithms are said to be loopless

Capital market pressures and the format of intellectual capital disclosure in intellectual capital intensive firms

Purpose - A number of studies have examined firms’ intellectual capital (IC) disclosure practices. However, the presentation format of IC disclosure (text, numerical and graphs/pictures) is yet to be examined. In addition, there is little evidence on the impact of capital market pressures on IC disclosure. This study aims to examine the relation between presentation format of IC disclosures and three market factors (market-to-book ratio, share price volatility and multiple listing. Design/methodology/approach - Using content analysis, we examine the level of IC disclosure provided in the annual reports of 100 IC-intensive listed UK firms. A 61-IC-item research instrument is used to measure IC disclosure and regression analysis is employed to examine the relation between disclosure and the market factors, controlling for corporate governance and firm specific variables. Findings - Text is the most commonly used format for IC disclosure, whilst the use of graphs/pictures is very low. The findings of the relation between market factors and IC disclosure are mixed. Market-to-book ratio is significantly related to disclosure in text and numerical, but not to graphs/pictures. Share price volatility is only associated with graphs/pictures, whilst multiple listing is only related to text. Originality/value - Our findings suggest that the impact of capital market pressures on IC disclosure might differ with presentation format. In this context, the study makes a significant contribution to the IC disclosure literature

Writing Reusable Digital Geometry Algorithms in a Generic Image Processing Framework

Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and algorithms. We propose an image processing framework focused on the Generic Programming paradigm in which an algorithm on the paper can be turned into a single code, written once and usable with various input types. This approach enables users to design and implement new methods at a lower cost, try cross-domain experiments and help generalize resultsComment: Workshop on Applications of Discrete Geometry and Mathematical Morphology, Istanb : France (2010