Algebraic Combinatorics and Coinvariant Spaces

ISBN-13: 9780367385460 / Angielski / Miękka / 2019 / 230 str.

Francois Bergeron

Opis

After recalling the basic notions of combinatorics, representation theory, and commutative algebra, the main material in this book provides links between the study of coinvariant/diagonally coinvariant spaces and the study of Macdonald polynomials and related operators. This gives rise to a large number of combinatorial questions relating to objects counted by familiar numbers, such as factorials, Catalan numbers, and the number of Cayley trees or parking functions. The author offers ideas for extending the theory to other families of finite Coxeter groups, besides permutation groups.

Spis treści

Combinatorial Objects. Some Tableau Combinatorics.　 Invariant Theory.　 Schur and Quasisymmetric Functions.　 Representation Theory.　 Species Theory.　 Commutative Algebra.　 Coinvariant Spaces.　 Macdonald Functions.　 Diagonal Coinvariant Spaces.　 Coinvariant-Like Spaces.　Formulary

O autorze

Bergeron, Francois