A rectangular drawing is a partition of a rectangle into a set of rectangles. Rectangular drawings have many important applications including VLSI layout. Since the size of rectangular drawings may be huge, compact encodings are desired. Several compact encodings of rectangular drawings without degree four vertices are known. In this paper, we design two compact encodings for rectangular drawin...

The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymtotically free with amalgamation over a subalgebra. Therefore we can define a “rectangular free convolution”, linearized by cumulants and by an analytic integral...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically free with amalgamation over a subalgebra. Therefore we can define a “rectangular free convolution”, linearized by cumulants and by an analytic integral...

In this paper, we connect rectangular free probability theory and spherical integrals. We prove the analogue, for rectangular or square non-Hermitian matrices, of a result that Guionnet and Mäıda proved for Hermitian matrices in [12]. More specifically, we study the limit, as n,m tend to infinity, of 1 n logE{exp[nmθXn]}, where θ ∈ R, Xn is the real part of an entry of UnMnVm, Mn is a certain n...