Related papers: Revitalized automatic proofs: demonstrations
The present work focuses on the study of the renowned Collatz conjecture, also known as the $3x +1$ problem. The distinguished analysis approach lies on the dynamics of an iterative map in binary form. A new estimation of the enlargement of…
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
In this paper we define a small variation of the Taylor method and a formula for the global error of this new numerical method that allows us to keep track of the round-off error and does not require previous knowledge of the exact…
In a recent article, Apagodu and Zeilberger (http://arxiv.org/abs/1606.03351)discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the…
On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
This is a thesis on some applications of regularly varying functions. Three problems are considered. The first problem is about the randomly weighted sums, the second is on the behavior of the product under conditional extreme value model…
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…
An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
In this note we demonstrate that a number of case-heavy combinatorial proofs in the mathematical phylogenetics literature can be proven more compactly using computational support. We use these techniques to also prove several new…
We refine Catalan numbers and Fu{\ss}-Catalan numbers by introducing colour statistics for triangulations of polygons and $d$-dimensional generalisations there-of which we call Fu{\ss}-Catalan complexes. Our refinements consist in showing…
We solve a problem of Marshal Hall by proving the convergence of the catalan number generating function directly on the basis of its recursion formula.
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We confirm a conjectural supercongruence involving Catalan numbers, which is one of the 100 selected open conjectures on congruences of Sun. The proof makes use of hypergeometric series identities and symbolic summation method.
Models of complicated systems can be represented in different ways - in scientific papers, they are represented using natural language text as well as equations. But to be of real use, they must also be implemented as software, thus making…
We analyze the combinatorics behind the operation of taking the logarithm of the generating function $G_k$ for $k^\text{th}$ generalized Catalan numbers. We provide combinatorial interpretations in terms of lattice paths and in terms of…