Related papers: Automated counting of LEGO towers
We use canonical Markov extensions (Hofbauer towers) to give an explicit construction of the natural extensions of various measure preserving endomorphisms, and present some applications to particular examples.
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…
This is a survey describing recents developments in enumerative geometry of curves on projective varieties. Various methods to arrive at results such as Kontsevich's formula for plane rational curves, or Caporaso-Harris's formula for plane…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules.…
Geometric modeling of multivariate reliability polynomials is based on algebraic hypersurfaces, constant level sets, rulings etc. The solved basic problems are: (i) find the reliability polynomial using the Maple and Matlab software…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WILFPLUS,…
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in…
An extension of the Tamari lattice to the multiplihedra is discussed, along with projections to the composihedra and the Boolean lattice. The multiplihedra and composihedra are sequences of polytopes that arose in algebraic topology and…
We introduce variants of Barvinok's algorithm for counting lattice points in polyhedra. The new algorithms are based on irrational signed decomposition in the primal space and the construction of rational generating functions for cones with…
We show how to translate the task of computing the multiplicative structure of a Chow ring of a projective homogeneous variety into an easily understandable combinatorial task of calculating in the corresponding polynomial ring. The…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…
A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a $O(n\log^2{n})$-time algorithm for deciding if a…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…