相关论文: Computational techniques for proving identities in…

This paper presents both a method and a result. The result presents a closed formula for the sum of the first $m+1,m \ge 0,$ squares of the sequence $F^{(k)}$ where each member is the sum of the previous $k$ members and with initial…

Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…

Symmetry reduction is crucial for solving many interesting SAT instances in practice. Numerous approaches have been proposed, which try to strike a balance between symmetry reduction and computational overhead. Arguably the most readily…

Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give…

The goal of this thesis is to advance the exploration of the statistical language learning design space. In pursuit of that goal, the thesis makes two main theoretical contributions: (i) it identifies a new class of designs by specifying an…

We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the…

The purpose of this paper is three-fold: first, we survey on several known pointwise identities involving fractional operators; second, we propose a unified way to deal with those identities; third, we prove some new pointwise identities in…

In this paper we establish two symmetric identities on sums of products of Euler polynomials.

This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…

We present an overview of the implementation of symmetric functions in MuPAD-Combinat. We also explain how to interface C++ programs with MuPAD in order to make efficient research during concrete work sessions.

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations…

We search for Nicomachean identities by adding translation parameters, variable parameters, sequence products and adjoining further numbers to sequences. The solutions of definite and indefinite quadratic forms arise in this study of cubic…

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…

We present a method for proving q-series identities by combinatorial telescoping, in the sense that one can transform a bijection or a classification of combinatorial objects into a telescoping relation. We shall illustrate this method by…

We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean $n\times n$-matrices and apply the characterization to computational complexity of identity checking, finite axiomatizability…

The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…

The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…