Edge Sequences, Ribbon Tableaux, and an Action of Affine Permutations

نویسنده

  • Marc A. A. van Leeuwen
چکیده

An overview is provided of some of the basic facts concerning rim hook lattices and ribbon tableaux, using a representation of partitions by their edge sequences. An action is defined of the affine Coxeter group of type Ãr−1 on the r-rim hook lattice, and thereby on the sets of standard and semistandard r-ribbon tableaux, and this action is related to the concept of chains in r-ribbon tableaux. 1991 Mathematics Subject Classification: 05E10.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spin-Preserving Knuth Correspondences for Ribbon Tableaux

The RSK correspondence generalises the Robinson-Schensted correspondence by replacing permutation matrices by matrices with entries in N, and standard Young tableaux by semistandard ones. For r ∈ N>0, the Robinson-Schensted correspondence can be trivially extended, using the r-quotient map, to one between r-coloured permutations and pairs of standard r-ribbon tableaux built on a fixed r-core (t...

متن کامل

ar X iv : 0 70 9 . 09 71 v 1 [ m at h . C O ] 6 S ep 2 00 7 k - RIBBON FIBONACCI TABLEAUX

We extend the notion of k-ribbon tableaux to the Fibonacci lattice, a differential poset defined by R. Stanley in 1975. Using this notion, we describe an insertion algorithm that takes k-colored permutations to pairs of k-ribbon Fibonacci tableaux of the same shape, and we demonstrate a colorto-spin property, similar to that described by Shimozono and White for ribbon tableaux. We give an evacu...

متن کامل

Arc Permutations ( extended abstract )

Arc permutations and unimodal permutations were introduced in the study of triangulations and characters. In this paper we describe combinatorial properties of these permutations, including characterizations in terms of pattern avoidance, connections to Young tableaux, and an affine Weyl group action on them. Résumé. Les permutations arc et les permutations unimodales ont été introduites dans l...

متن کامل

Combinatorics of Ribbon Tableaux

This thesis begins with the study of a class of symmetric functions {x} which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators on the space of partitions. I develop the theory of ribbon functions using these operators in an ...

متن کامل

Standard Young tableaux for finite root systems

Abstract. The study of representations of affine Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any finite Coxeter group. This paper is completely independent of affine Hecke algebra theory and is purely combinatorial. We define generalized shapes and standard Young tableaux and show that these new objects coincide with the classi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Eur. J. Comb.

دوره 20  شماره 

صفحات  -

تاریخ انتشار 1999