In this article, we derive bounds for values of the global geometry of locally tessellating planar graphs, namely, the Cheeger constant and exponential growth, in terms of combinatorial curvatures. We also discuss spectral implications for the Laplacians.

Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of equational axioms the first order theory override on resolving main unsolved problem area.

Since the 1970s, the study of torus actions has become increasingly important in various areas of pure mathematics, and has stimulated the formation of interdisciplinary links between algebraic geometry, combinatorial and convex geometry, commutative and homological algebra, differential topology and homotopy theory. As their net has spread wider, and the literature grown, a field of activity h...

In this paper, we introduce combinatorially defined subvarieties of symplectic flag varieties called symplectic restriction varieties. We study their geometric properties and compute their cohomology classes. In particular, we give a positive, combinatorial, geometric branching rule for computing the map in cohomology induced by the inclusion i : SF (k1, . . . , kh;n) → F (k1, . . . , kh;n). Th...