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

We present a new proof of Stembridge's theorem about the enumeration of totally symmetric plane partitions using the methodology suggested in the recent Koutschan-Kauers-Zeilberger semi-rigorous proof of the Andrews-Robbins q-TSPP…

We announce a new four parameter partition theorem from which the (big) theorem of Gollnitz follows by setting any one of the parameters equal to 0. This settles a problem of Andrews who asked whether there exists a result that goes beyond…

We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.

We present a quantum probabilistic algorithm which tests with a polynomial computational complexity whether a given composite number is of the Carmichael type. We also suggest a quantum algorithm which could verify a conjecture by…

In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…

We introduce the concept of disjunctive sum of squares for certifying nonnegativity of polynomials. Unlike the popular sum of squares approach where nonnegativity is certified by a single algebraic identity, the disjunctive sum of squares…

We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.

We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous…

Using sequences of finite length with positive integer elements and the inversion statistic on such sequences, a collection of binomial and multinomial identities are extended to their $q$-analog form via combinatorial proofs. Using the…

In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology,…

In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…

Quorum systems are a key mathematical abstraction in distributed fault-tolerant computing for capturing trust assumptions. A quorum system is a collection of subsets of all processes, called quorums, with the property that each pair of…

Exact rational partitions are presented for Bernoulli and Euler numbers as novel sums involving Faulhaber and Sali\'e coefficients.

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…

We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity, Rogers-Ramanujan identities, and some identities of Rogers. We give a tiling proof of the…

The software package developed in the MS thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized…

A Goellnitz-Gordon partition is one in which the parts differ by at least 2, and where the inequality is strict if a part is even. Let Q_i(n) denote the number of partitions of n into distinct parts not congruent to i mod 4. By attaching…

We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of the complex plane and D an effective divisor supported on the boundary of…

We use computer algebra to study polynomial identities for the trilinear operation [a,b,c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a,b,c] satisfies the alternating property in degree 3, no new…