Local Constructive Set Theory (LCST) is intended to be a local version of constructive set theory (CST). Constructive Set Theory is an open-ended set theoretical setting for constructive mathematics that is not committed to any particular brand of constructive mathematics and, by avoiding any built-in choice principles, is also acceptable in topos mathematics, the mathematics that can be carrie...

In this paper we provide constructive proofs that the following three statistics are equidistributed: the number of ascent plateaus of Stirling permutations of order n, a weighted variant of the number of excedances in permutations of length n and the number of blocks with even maximal elements in perfect matchings of the set {1, 2, 3, . . . , 2n}.

The Strang and Fix conditions relate the accuracy of a finite element method to its ability to reproduce polynomials. A similar condition is proved to exist for the approximation of the product on these finite elements. Piecewise polynomial approximations are studied further, including a constructive description of all related approximate product operators.

Let G be a connected linear algebraic group, let V be a finite dimensional algebraic G-module, and let a and b be two elements of V . We describe a constructive way to find out whether the G-orbit of a lies in the closure of the G-orbit of b.

M.C. Escher illustrated his mathematical investigations of the constructive elements of this world in a form of two-dimensional drawings, which inspired many computer scientists to make computer reproductions and reconstructions. We introduce unusual higher-dimensional computer reconstructions to illustrate our research results in geometric modeling problems arising from analysis of Escher’s ar...

We define higher order fixed points of normal functions, describe them and apply to obtain a constructive proof that, if κ is the least ordinal such that the ultrapower κ/F is non-trivial, then that ultrapower has at least κ elements. AMS Mathematics Subject Classification (2000): 03E04, 03E20, 03C20.

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multi-loop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.

Stanley conjectured in 1977 that the h-vector of a matroid simplicial complex is a pure O-sequence. We give simple constructive proofs that the conjecture is true for matroids of rank less than or equal to 3, and corank 2. We used computers to verify that Stanley’s conjecture holds for all matroids on at most nine elements.

In this work we describe an algorithm that generates well constrained geometric constraint graphs which are solvable by the treedecomposition constructive technique. The algorithm is based on Henneberg constructions and would be of help in transforming underconstrained problems into well constrained problems as well as in exploring alternative constructions over a given set of geometric elements.

Suppose ∆C,E ∼= e. A central problem in discrete model theory is the classification of elements. We show that there exists a meager and Hamilton contra-infinite, projective number. We wish to extend the results of [15] to linearly projective subgroups. U. Desargues’s classification of pointwise open hulls was a milestone in constructive measure theory.