Infinite decomposition bases

Connected Hopf Algebras with Dixmier Bases and Infinite Primary Decomposition

Bases in Infinite Matroids

We consider bases in matroids of infinite rank, and prove: (a) the existence of a perfect matching in the 'transition graph' of any two bases. This is an extension of the existence of a non-zero generalized diagonal in the transition matrix between bases in finite dimensional linear spaces, and settles a conjecture of the second author [8]. (b) A Cantor-Bernstein theorem for matroids. (c) The e...

Infinite Multi-bases

Infinite multi-bases can have infinite and multiple type declarations for the same variable. They can be used as a proof-technique to manipulate only one common basis along the proof. However, no proper definition and precise study of typed lambda calculus with infinite multi-bases appear in the literature. This paper introduces type assignment systems with infinite multi-bases and studies the ...

Pommaret Bases and Rees Decomposition

We define involutive bases for polynomial ideals and demonstrate their use in calculating direct decompositions of polynomial modules, focusing on the so-called Pommaret bases. The resulting decomposition is the well known Rees decomposition. An overview of other important applications of Pommaret bases is given.

Decomposition numbers and canonical bases

We obtain some simple relations between decomposition numbers of quantized Schur algebras at an nth root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a decomposition number for some Hecke algebra of type A. We prove similar relations between coefficients of the canonical basis of the q-deformed Fock space repres...