Crops of the parkland – Yorkton, Saskatchewan

Non-Peer Reviewe

Combinatorial interpretation and positivity of Kerov's character polynomials

Kerov's polynomials give irreducible character values in term of the free cumulants of the associated Young diagram. We prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. Our method, through decomposition of maps, gives a description of the coefficients of the k-th Kerov's polynomials using permutations in S(k). We also obtain explicit formulas or combinatorial interpretations for some coefficients. In particular, we are able to compute the subdominant term for character values on any fixed permutation (it was known for cycles).Comment: 33 pages, 13 figures, version 3: minor modifcation

Age of Rotational Landslides in the Cypress Hills, Alberta-Saskatchewan

The topography of the west block of the Cypress Hills indicates that fluvial dissection of the plateaux and subsequent rotational landsliding of valley sides have been the dominant Quaternary geomorphic processes. This paper presents a preliminary chronology of rotational landslides based on the relative ages of 17 landslides and on 3 absolute dates. Four indices of relative age were used: organic content in Ah and B soil horizons, the size and coverage of lichens and weathering rind thickness on boulders exposed by landsliding, and the concavity and gradient of gullies in landslide debris, One landslide occurred in 1965. Organic materials collected from buried soil horizons beneath depressions on 3 other landslides were radiocarbon dated at 1235 ± 105, 1635 ± 105 and 7259 ± 165 yrs. BP. Microscopic analysis of the organic material revealed that the oldest sample was contaminated with older carbon. Cluster analysis of the relative age data in conjunction with 3 acceptable absolute dates suggests that the landslides under study have occurred during late Holocene time.La topographie du secteur ouest des Cypress Hills révèle qu'au Quaternaire les principaux processus géomorphologiques ont été l'érosion fluviatile, sur les plateaux, et les glissements de terrain par rotation, sur les versants. Le présent article propose une chronologie des glissements de terrain, 17 ayant une datation relative, et 3, une datation absolue. Quatre indices ont été utilisés pour déterminer l'âge relatif: la teneur en matière organique des horizons pédologiques Ah et B, la concavité et la pente des ravins creusés dans les matériaux, la taille des lichens et Ia surface qu'ils occupent sur des blocs mis au jour par les glissements de terrain, ainsi que l'épaisseur de la couche altérée sur ces blocs. Il y eut un glissement en 1965. À la suite du prélèvement de matière organique dans des horizons pédologiques enfouis, on a pu dater au radiocarbone trois autres glissements (1235 ± 105; 1635 ± 105; 7259 ± 165 BP). L'analyse des échantillons au microscope révèle que Ia matière organique la plus ancienne renfermait du carbone. Une analyse d'ensemble (datations relatives et absolues) laisse penser que les glissements de terrain se sont produits à la fin de l'Holocène.Die Topographie des Westteils der Cypress Hills IaBt erkennen, daB die fluviatile Gliederung der Plateaus und anschlieBende Erdrutsche der Talseiten die wichtigsten geomorphologischen Prozesse im Quaternâr gewesen sind. Dieser Artikel gibt eine vorlâufige Chronologie der Erdrutsche, gestùtzt auf die relative Datierung von 17 Erdrutschen und auf drei absolute Datierungen. Vier Anhaltspunkte wurden fur die relative Datierung benutzt: Der organische Gehalt in den Ah und B Boden-Horizonten, die GrôBe und Ausdehnung der Flechten und die Dicke der Verwitterungskruste auf den durch die Erdrutsche bloBgelegten Blôcken und die Hôhlung und Neigung der Rinnen in den Erdrutsch-Gesteinstrùmmern. Ein Erdrutsch ereignete sich 1965. Organisches Material, das aus vergrabenen Boden-Horizonten unterhalb der Senken von drei anderen Erdrutschen stammt, wurde mit Radiokarbon auf 1235 ± 105, 1635 ± 105 und 7259 ± 165 Jahre BP datiert. Die mikroskopische Analyse des organischen Materials lieB erkennen, daB die àlteste Probe àlteren Kohlenstoff enthielt. Eine Block-Analyse der relativen Datierungen im Zusammenhang mit den drei annehmbaren absoluten Datierungen legt nahe, daB die untersuchten Erdrutsche wâhrend des spâten Holozàn stattgefunden haben

Towards the geometry of double Hurwitz numbers

AbstractDouble Hurwitz numbers count branched covers of CP1 with fixed branch points, with simple branching required over all but two points 0 and ∞, and the branching over 0 and ∞ specified by partitions of the degree (with m and n parts, respectively). Single Hurwitz numbers (or more usually, Hurwitz numbers) have a rich structure, explored by many authors in fields as diverse as algebraic geometry, symplectic geometry, combinatorics, representation theory, and mathematical physics. The remarkable ELSV formula relates single Hurwitz numbers to intersection theory on the moduli space of curves. This connection has led to many consequences, including Okounkov and Pandharipande's proof of Witten's conjecture.In this paper, we determine the structure of double Hurwitz numbers using techniques from geometry, algebra, and representation theory. Our motivation is geometric: we give evidence that double Hurwitz numbers are top intersections on a moduli space of curves with a line bundle (a universal Picard variety). In particular, we prove a piecewise-polynomiality result analogous to that implied by the ELSV formula. In the case m=1 (complete branching over one point) and n is arbitrary, we conjecture an ELSV-type formula, and show it to be true in genus 0 and 1. The corresponding Witten-type correlation function has a richer structure than that for single Hurwitz numbers, and we show that it satisfies many geometric properties, such as the string and dilaton equations, and an Itzykson–Zuber-style genus expansion ansatz. We give a symmetric function description of the double Hurwitz generating series, which leads to explicit formulae for double Hurwitz numbers with given m and n, as a function of genus. In the case where m is fixed but not necessarily 1, we prove a topological recursion on the corresponding generating series, which leads to closed-form expressions for double Hurwitz numbers and an analogue of the Goulden–Jackson polynomiality conjecture (an early conjectural variant of the ELSV formula). In a later paper (Faber's intersection number conjecture and genus 0 double Hurwitz numbers, 2005, in preparation), the formulae in genus 0 will be shown to be equivalent to the formulae for “top intersections” on the moduli space of smooth curves Mg. For example, three formulae we give there will imply Faber's intersection number conjecture (in: Moduli of Curves and Abelian Varieties, Aspects of Mathematics, vol. E33, Vieweg, Braunschweig, 1999, pp. 109–129) in arbitrary genus with up to three points

Improving scenario methods in infrastructure planning: a case study of long distance travel and mobility in the uk under extreme weather uncertainty and a changing climate

This paper develops a mixed method approach to infrastructure planning through a United Kingdom (UK) case study examining the impact of a changing climate on long distance travel and mobility between London and Glasgow. A novel combination of a qualitative method - Systematic Qualitative Foresight (SQF) - and quantitative simulation using discrete choice stated preference methods is applied. The main dataset is a travel behaviour survey of over 2,000 residents of London and Glasgow. Three illustrative SQF-based scenarios are developed incorporating society, technology and climate dimensions. For each scenario, the choice of long-distance travel mode by two groups of respondents generated by cluster analysis is simulated using stated preference survey data to describe the choices likely to be made by actors within each scenario. We demonstrate the importance of considering a wide range of variables when creating instruments for infrastructure planning decisions. Our results show that weather-related disruption has consequences for travel behaviour, with a considerable number of travellers deciding not to travel despite the importance of their trip. However, the vast majority of travellers would still travel. This should be considered by policy makers, and those responsible for transport infrastructure, in order to increase its resilience to extreme weather and demand, and better devise contingencies plans to contain, and minimise, the effect of the disruptions on the users. The method described has wider implications for infrastructure planning, particularly in its ability to engage a broader range of stakeholders and to avoid linear models of prediction. By emphasising the creation of a plausible decision space, it offers the possibility of increased robustness and resilience in infrastructure planning