Generalizations and refinements of a partition theorem of Göllnitz.
Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions.
Generalizations of Schur's partition theorem.
Generalizing the combinatorics of binomial coefficients via -nomials.
Generating function for -restricted jagged partitions.
Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials
We prove that the monoid of generic extensions of finite-dimensional nilpotent k[T]-modules is isomorphic to the monoid of partitions (with addition of partitions). This gives us a simple method for computing generic extensions, by addition of partitions. Moreover we give a combinatorial algorithm that calculates the constant terms of classical Hall polynomials.