Related papers: Encoding toroidal triangulations
We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with a simple boundary. As a consequence, we count the number of…
We extend the notion of canonical ordering (initially developed for planar triangulations and 3-connected planar maps) to cylindric (essentially simple) triangulations and more generally to cylindric (essentially internally) $3$-connected…
We survey recent developments in the study of torus equivariant motivic Chern and Hirzebruch characteristic classes of projective toric varieties, with applications to calculating equivariant Hirzebruch genera of torus-invariant Cartier…
A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…
In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab. 39 (2011) 2224-2270]…
We compute the number of triangulations of a convex $k$-gon each of whose sides is subdivided by $r-1$ points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as $k$ and/or $r$…
Nature is imbued with mathematics, manifested through its stunning patterns, symmetries, and structures. Here, we unveil that in a multilayered framework of twisted birefringent optical components, a recursive number pattern of Pascal's…
The triangulations of a regular convex polygon are enumerated according to the number of diagonals parallel to a fixed edge. The enumeration uses the Shapiro convolution identity, as well as an interpretation of this identity in terms of…
Harmonic mappings have long intrigued researchers due to their intrinsic connection with minimal surfaces. In this paper, we investigate shearing of two distinct classes of univalent conformal mappings which are convex in horizontal…
We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
Image triangulation, the practice of decomposing images into triangles, deliberately employs simplification to create an abstracted representation. While triangulating an image is a relatively simple process, difficulties arise when…
This paper presents a new method to generate tool paths for machining freeform surfaces represented either as parametric surfaces or as triangular meshes. This method allows for the optimal tradeoff between the preferred feed direction…
3-manifolds are commonly represented as triangulations, consisting of abstract tetrahedra whose triangular faces are identified in pairs. The combinatorial sparsity of a triangulation, as measured by the treewidth of its dual graph, plays a…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
A spinorial approach to 6-dimensional differential geometry is constructed and used to analyze tensor fields of low rank, with special attention to the Weyl tensor. We perform a study similar to the 4-dimensional case, making full use of…
An elementary geometric construction known as Napoleon's theorem produces an equilateral triangle built on the sides of any initial triangle: the centroids of each equilateral triangle meeting the original sides, all outward or all inward,…
We present a direct bijection between planar 3-connected triangulations and bridgeless planar maps, which were first enumerated by Tutte (1962) and Walsh and Lehman (1975) respectively. Previously known bijections by Wormald (1980) and Fusy…
In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…
Billey and Braden defined a geometric pattern map on flag manifolds which extends the generalized pattern map of Billey and Postnikov on Weyl groups. The interaction of this torus equivariant map with the Bruhat order and its action on line…