77,626 research outputs found
The Probably and the Provable. By Jonathan L. Cohen
 Sight: LĂ„ngholmen, Stockhomen âLĂ„ngholmensmarinstadâ bestĂ„r av tre delar. En bĂ„tuppstĂ€llningslada ett bostadsomrĂ„de och en restaurang. BĂ„tuppstĂ€llningsladan har Ă€ven en dubbel funktion som teater under sommar halvĂ„ret dĂ„ Stockholmstads Parkteater fĂ„r en fast spelplats och bĂ„tarna ligger i vattnet. Restarangen ligger i anslutning till bĂ„t huset och har en stor glas vĂ€gg som öppnar sig in mot BĂ„tarna/teatern som skapar ett tydligt marint tema.  BostadsomrĂ„det bestĂ„r av nio stycken radhus som vilar mot den befintliga Q-mĂ€rkta fĂ€ngelsemuren likt smĂ„ japanskavillor med ljusgĂ„rd. Det centralt placerade bostadshuset med sina fem vĂ„ningar Ă€r lika högt som de gamla fĂ€ngelsebyggnaderna. En lugn lummig innergĂ„rd skapas emellan radhus och bostadshuset. Den lokala segel skolan fĂ„r Ă€ven husera i den nedre vĂ„ningen av bostadshuset.    Sight: LĂ„ngholmen, Stockhomen âLĂ„ngholmensmarinstadâ 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 storyâs 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
- âŠ