Related papers: Zeilberger to the rescue
Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly $k$ times and the remaining parts are not repeated. They presented several interesting results and posed questions…
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
Large Language Models (LLMs) have demonstrated remarkable emergent capabilities, yet the robustness of their numerical reasoning remains an open question. While standard benchmarks evaluate LLM reasoning on complex problem sets using…
Recursive matrices are ubiquitous in combinatorics, which have been extensively studied. We focus on the study of the sums of $2\times 2$ minors of certain recursive matrices, the alternating sums of their $2\times 2$ minors, and the sums…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing…
Recently, the covariant formulation of the geometric bifurcation theory, developed in a previous paper, has been applied to two elementary problems: the study of limit cycles of dynamical systems and the second part of Hilbert's sixteenth…
We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…
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…
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of algebraic problems often results in nonisolated singular…
L. Weinstein's brilliant short proof of de Branges's Theorem is made even shorter by using computer algebra.
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
I discuss issues of inverting feasibly computable functions, optimal discovery algorithms, and the constant overheads in their performance.
Simple memorizing tasks have been chosen such as a binary code on a matrix. After the establishment of an appropriate protocol, the codified matrices were individually presented to 150 university students who had to memorize them. A…
The class of solvable many-body problems "of goldfish type" is extended by including (the additional presence of) three-body forces. The solvable $N$-body problems thereby identified are characterized by Newtonian equations of motion…
Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and $4$-regular partitions follow. In…