Related papers: Enumerative combinatorics package for CoCoA
We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed,…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the…
We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides…
In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combinatorics. Topics include geometric modeling in…
We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
We introduce a Markov Chain Monte Carlo simulation and data analysis package that extends the CMBEASY software. We have taken special care in implementing an adaptive step algorithm for the Markov Chain Monte Carlo in order to improve…
Although the P\'olya enumeration theorem has been used extensively for decades, an optimized, purely numerical algorithm for calculating its coefficients is not readily available. We present such an algorithm for finding the number of…
We present a simple package for distributing evaluations of a Mathematica function for many arguments on a cluster of computers. After setting up the hosts, the only change is to replace Map[f,points] by MapCore[f,points].
We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum…
The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this…
We present the new R package CoinCalc for performing event coincidence analysis (ECA), a novel statistical method to quantify the simultaneity of events contained in two series of observations, either as simultaneous or lagged coincidences…
Principal component analysis (PCA) is routinely used in population genetics to assess genetic structure. With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies…
The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the…
Polya Enumeration Theorem is one of the most useful tools dealing with the enumeration of patterns that are symmetric in some ways. What follows is a procedure for obtaining the results of Polya Theorem directly, bypassing the usual…
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
This work introduces a new software package `Sesame' for the numerical computation of classical semiconductor equations. It supports 1 and 2-dimensional systems and provides tools to easily implement extended defects such as grain…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…