相关论文: A computer proof of a polynomial identity implying…

With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric…

In this paper, we prove a theorem which adds a new member to the famous G\"oellnitz-Gordon identities. We construct a "new system of recurrence formulas" in order to prove it.

We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF…

Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…

Here, we establish a polynomial identity in three variables $a, b, c$, and with the degree of the polynomial given in terms of two integers $L, M$. By letting $L$ and $M$ tend to infinity, we get the 1993 Alladi-Gordon $q$-hypergeometric…

We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…

We will prove an identity involving refined $q$-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined $q$-trinomials in an…

We present a combinatorial proof of the $q$-Pfaff--Saalsch\"utz identity by a composition of explicit bijections, in which $q$-binomial coefficients are interpreted as counting subspaces of $\mathbb{F}_q$-vector spaces. As a corollary, we…

Alladi and Gordon introduced the method of weighted words in 1993 to prove a refinement and generalisation of Schur's partition identity. Together with Andrews, they later used it to refine Capparelli's and G\"ollnitz' identities too. In…

We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…

In this work, we describe our experience in learning the use of a computer proof assistant - specifically, Lean - from scratch, through proving formulae for the solutions of polynomial equations. Specifically, in this work we characterize…

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…

Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…

Recently, Andrews and EI Bachraoui discovered several companions for some famous $q$-series formulas, and derived some new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results…

Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include…

We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…

I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…

In this paper we formulate combinatorial identities that give representation of positive integers as linear combination of even powers of 2 with binomial coefficients. We present side by side combinatorial as well as computer generated…

In this article algorithmic methods are presented that have essentially been introduced into computer algebra systems like Mathematica within the last decade. The main ideas are due to Stanley and Zeilberger. Some of them had already been…

We prove a partition identity conjectured by Lassalle (Adv. in Appl. Math. 21 (1998), 457-472).