The Probably and the Provable. By Jonathan L. Cohen

  Sight: Långholmen, Stockhomen ”Långholmensmarinstad” består av tre delar. En båtuppställningslada ett bostadsområde och en restaurang. Båtuppställningsladan har även en dubbel funktion som teater under sommar halvåret då Stockholmstads Parkteater får en fast spelplats och båtarna ligger i vattnet. Restarangen ligger i anslutning till båt huset och har en stor glas vägg som öppnar sig in mot Båtarna/teatern som skapar ett tydligt marint tema.   Bostadsområdet består av nio stycken radhus som vilar mot den befintliga Q-märkta fängelsemuren likt små japanskavillor med ljusgård. Det centralt placerade bostadshuset med sina fem våningar är lika högt som de gamla fängelsebyggnaderna. En lugn lummig innergård skapas emellan radhus och bostadshuset. Den lokala segel skolan får även husera i den nedre våningen av bostadshuset.      Sight: Långholmen, Stockhomen ”Långholmensmarinstad” consists of three parts. These are a large boathouse housing complex and a restaurant. The boathouse also has a double function as theatre space during the summer months when the Stockholm Parkteatern needs its seasonal venue. The restaurant is in direct adjacent to the Boathouse/theatre with a large glass wall which gives the restaurant a natural marina vibe. The housing complex consists of nine townhouses adjacent to the old heritage labelled prison wall, with small Japanese courtyards and one housing block. The housing block rises five story’s and has the same metric height as the surrounding historical prison buildings.   This creates a green peaceful inner courtyard in-between the townhouses and the housing block. The locale yachting club is given a natural haven in the ground floor space in the housing block

Rank three matroids are Rayleigh

A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.Comment: 11 pages, 3 figures, 3 table

Algebras related to matroids represented in characteristic zero

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the structure of these algebras. In return, the numerical properties of the Hilbert function of A yield some information about the Tutte polynomial of the corresponding matroid. Isomorphism classes of these algebras correspond to equivalence classes of hyperplane arrangements under the action of the general linear group.Comment: 11 pages AMS-LaTe

The algebra of flows in graphs

We define a contravariant functor K from the category of finite graphs and graph morphisms to the category of finitely generated graded abelian groups and homomorphisms. For a graph X, an abelian group B, and a nonnegative integer j, an element of Hom(K^j(X),B) is a coherent family of B-valued flows on the set of all graphs obtained by contracting some (j-1)-set of edges of X; in particular, Hom(K^1(X),R) is the familiar (real) ``cycle-space'' of X. We show that K(X) is torsion-free and that its Poincare polynomial is the specialization t^{n-k}T_X(1/t,1+t) of the Tutte polynomial of X (here X has n vertices and k components). Functoriality of K induces a functorial coalgebra structure on K(X); dualizing, for any ring B we obtain a functorial B-algebra structure on Hom(K(X),B). When B is commutative we present this algebra as a quotient of a divided power algebra, leading to some interesting inequalities on the coefficients of the above Poincare polynomial. We also provide a formula for the theta function of the lattice of integer-valued flows in X, and conclude with ten open problems.Comment: 31 pages, 1 figur