Related papers: Zeilberger to the rescue
With the recent rise of widely successful deep learning models, there is emerging interest among professionals in various math and science communities to see and evaluate the state-of-the-art models' abilities to collaborate on finding or…
In this article we address the problem of automatic answer checking in interactive learning systems that support mathematical notation. This problem consists of the problem of establishing identities in formal mathematical systems and hence…
In this paper, we prove that every pair of sufficiently large odd integers can be represented in the form of a pair of one prime, four prime cubes and $48$ powers of $2$.
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result using an analysis of the six-vertex state model (also called…
We report new results on eight problems in mathematics and theoretical computer science, produced with the assistance of Bolzano, an open-source multi-agent LLM system. Bolzano orchestrates rounds of interaction between parallel prover…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a…
We use the Wilf-Zeilberger method to prove identities between Mahler measures of polynomials. In particular, we offer a new proof of a formula due to Lal\'{i}n, and we show how to translate the identity into a formula involving elliptic…
Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Kennedy and O'Hagan \cite{kennedy2001bayesian} suggested an approach to estimate them by using…
Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…
Enumeration problems related to words avoiding patterns as well as permutations that contain the pattern $123$ exactly once have been studied in great detail. However, the problem of enumerating words that contain the pattern $123$ exactly…
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This…
We introduce the Binary Matrix Guessing Problem and provide two algorithms to solve this problem. The first algorithm we introduce is Elementwise Probing Algorithm (EPA) which is very fast under a score which utilizes Frobenius Distance.…
We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions…
We show equivalences between several high-dimensional problems in extremal combinatorics and parallel repetition of multiplayer (multiprover) games over large answer alphabets. This extends the forbidden-subgraph technique, previously…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
In this paper we consider a few Calculus optimization problems in which we notice peculiar patterns. In each of these cases there is a geometric explanation for the pattern showing that it is not just a coincidence.
This paper is a sequel of arXiv:2109.06394. In this paper, we consider a kind of inverse problem of multipliers. The problem is to count number of isospectral correspondences, correspondences which has the same combination of multipliers.…