Generators for $A(\Omega )$

Standard Generators for J3

Minimal Generators for Symmetric Ideals

Let R = K[X] be the polynomial ring in infinitely many indeterminates X over a field K, and let SX be the symmetric group of X. The group SX acts naturally on R, and this in turn gives R the structure of a module over the group ring R[SX ]. A recent theorem of Aschenbrenner and Hillar states that the module R is Noetherian. We address whether submodules of R can have any number of minimal gener...

Random-number Generators Physical Random-number Generators

R andom numbers have applications in many areas: simulation, game-playing, cryptography, statistical sampling, evaluation of multiple integrals, particletransport calculations, and computations in statistical physics, to name a few. Since each application involves slightly different criteria for judging the “worthiness” of the random numbers generated, a variety of generators have been develope...

Generators and Relations for K

Tate’s algorithm for computing K2OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order—the latter, together with some structural results on the p-primary part of K2OF due to Tate and Keune, gives a proof of its structure for many number fields of small discriminants, confirming earlier conjectural...

Scoping Constructs for Program Generators

Program generation is the process of generating code in a high-level language (e.g., C, C++, Java) to implement an abstract specification of a program. Generated programs are created by synthesizing and composing code fragments. Binding identifiers in generated code with their correct variable declarations has been the focus of a lot of research work in the context of macro-expansion (e.g., hyg...