The absolute order on the hyperoctahedral group

The absolute order on the hyperoctahedral group B n is investigated. Using a poset fiber theorem, it is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen-Macaulay. This method results in a new proof of Cohen-Macaulayness of the absolute order on the symmetric group. Moreover, it is shown that every closed interval in the absolute order on B n is shellable and an example of a non-Cohen-Macaulay interval in the absolute order on D 4 is given. Finally, the closed intervals in the absolute order on B n and D n which are lattices are characterized and some of their important enumerative invariants are computed. © 2010 Springer Science+Business Media, LLC

The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes

The absolute order is a natural partial order on a Coxeter group W. It can be viewed as an analogue of the weak order on W in which the role of the generating set of simple reflections in W is played by the set of all reflections in W. By use of a notion of constructibility for partially ordered sets, it is proved that the absolute order on the symmetric group is homotopy Cohen-Macaulay. This answers in part a question raised by V. Reiner and the first author. The Euler characteristic of the order complex of the proper part of the absolute order on the symmetric group is also computed. © 2008 Elsevier Inc. All rights reserved

Simply connected homogeneous continua are not separated by arcs

We show that locally connected,simply connected homogeneous continua are not separated by arcs. We ask several questions about homogeneous continua which are inspired by analogous questions in geometric group theory. © 2007 Elsevier B.V. All rights reserved

Edgewise cohen-macaulay connectivity of partially ordered sets

Ihc proper parts of Face lattices of convex poly to pes are shown to satisfy a strong form of the Cohcn-Macaulay property, namely that removing from their Hassc diagram all edges in any closed interval results in a Cohen.Macau I ay posel of the same rank. A corresponding notion of edgewise Cohcn-Macaulay eonnecliviiy for paitially ordered sets is investigated. Examples and open questions arc discussed. © 2018 Mathematica Scandinavica. All rights reserved

A Cable Laid Is a Cable Played : On the Hibernation Logic behind Urban Infrastructure Mines

Our societies are reliant on metals to such an extent that the total amounts of some of them in the built environment are comparable in size to the remaining amounts in known mountain ores. Because of concerns about mineral scarcity, the United Nations has assessed alternative sources for metal extraction and targeted urban areas in general and infrastructure systems in particular, since these are large, spatially concentrated and rich in metals. Referring to the possibility of recovering these metal stocks, infrastructure systems constitute what material flow researchers has conceptually termed “urban mines.” While most urban infrastructure is in use, significant amounts of cables and pipes have been disconnected and remain in their subsurface locations; they are “hibernating.” In this article, we analyze the occurrence of such hibernation in the Swedish city of Norrköping's urban infrastructure mine where, we know from a previous study, that every fourth kilo of infrastructure is discarded. Our applied perspective is different from the logic of system expansion as a way to meet increased demand often found in the field of infrastructure studies since we are interested in how systems are disconnected and left behind. This enables us to offer a refined understanding of the concepts of infrastructure “decline” and infrastructure “cold spots.” We argue that to prevent the increase of dormant infrastructures and to engage in the urban mining of already dormant infrastructures, we must develop a sensibility to the materiality of derelict infrastructure components and the underlying causes for why they form different kinds of spatial patterns