A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The proposed partition joins together ideas of the Seven Triangle Longest-Edge partition (7T-LE), and the classical criteria for constructing Delaunay meshes. The new partition performs similarly compared to the Delaunay triangulation (7T-D) with the benefit of being more robust and...

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite ...

We prove the following finite generator theorem. Let G be a countable group acting ergodically on a standard probability space. Suppose this action admits a generating partition having finite Shannon entropy. Then the action admits a finite generating partition. We also discuss relationships between generating partitions and f-invariant and sofic entropies.

We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.

We consider generalizations of the honeycomb problem to the sphere S and seek the perimeter-minimizing partition into n regions of equal area. We provide a new proof of Masters’ result that three great semicircles meeting at the poles at 120 degrees minimize perimeter among partitions into three equal areas. We also treat the case of four equal areas, and we prove under various hypotheses that ...

This paper gives a proof of the classical honeycomb conjecture: any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling.

The Standard Simplex Conjecture of Isaksson and Mossel [12] asks for the partition {Ai}i=1 of R into k ≤ n + 1 pieces of equal Gaussian measure of optimal noise stability. That is, for ρ > 0, we maximize k ∑

For a subfamily of multiplicative measures on integer partitions we give conditions for associated Young diagrams to converge in probability after a proper rescaling to a certain curve named the limit shape of partitions. We provide explicit formulas for the scaling function and the limit shape covering some known and some new examples. Introduction It is now widely known that a random partitio...

We consider the problem of dividing a geographic region into sub-regions so as to minimize the maximum workload of a collection of facilities over that region. We assume that the cost of servicing a demand point is a monomial function of the distance to its assigned facility and that demand points follow a continuous probability density. We show that, when our objective is to minimize the maxim...