By Kurt Luoto, Stefan Mykytiuk, Stephanie van Willigenburg

Show description

Read Online or Download An Introduction to Quasisymmetric Schur Functions (September 26, 2012) PDF

Similar introduction books

Exceptional Learners: An Introduction to Special Education.

Unparalleled novices is an exceptional advent to the features of remarkable rookies and their schooling, emphasizing school room practices in addition to the mental, sociological, and scientific points of disabilities and giftedness. in line with this period of responsibility, all discussions and examples of academic practices are grounded in a legitimate learn base.

Introduction to avionics systems

Advent to Avionic structures, moment version explains the rules and concept of contemporary avionic platforms and the way they're applied with present know-how for either civil and army airplane. The structures are analysed mathematically, the place applicable, in order that the layout and function might be understood.

Additional info for An Introduction to Quasisymmetric Schur Functions (September 26, 2012)

Sample text

4 The Hopf algebra of noncommutative symmetric functions Our third and final Hopf algebra involves noncommutative symmetric functions, defined by Gelfand et al. in [34]. As we will see, they are closely connected to both quasisymmetric and symmetric functions. Throughout we use the notation used in [11], which evokes the relationship with symmetric functions. 1. The Hopf algebra of noncommutative symmetric functions, denoted by NSym, is Q e1 , e2 , . . generated by noncommuting indeterminates en of degree n with the operations of the next subsection.

Given two permutations σ = σ (1) · · · σ (n) ∈ Sn and τ = τ(1) · · · τ(m) ∈ Sm , we say a shuffle of σ and τ is a permutation in Sn+m such that σ (i) appears to the right of σ (i − 1) and to the left of σ (i + 1) for all 2 i n − 1 and similarly, τ(i) + n appears to the right of τ(i − 1) + n and to the left of τ(i + 1) + n for all 2 i m − 1. We denote by σ τ the set of all shuffles of σ and τ. 8. 12 Let α Then n, β ✁ 21 = {1243, 1423, 1432, 4123, 4132, 4312}. m and σ ∈ Sn , τ ∈ Sm , such that d(σ ) = set(α) and d(τ) = set(β ).

Let λ = (5, 4, 2, 2). Below is the Young diagram of λ , with the label γλ (i, j) written in the cell with coordinate pair (i, j). 40 3 Hopf algebras 1 5 2 6 3 7 9 4 8 10 12 11 13 Let T be an SSYT of shape λ . If we regard T as the map from Pλ to the positive integers that sends the pair (i, j) to the entry of the cell with coordinate pair (i, j), then T is a (Pλ , γλ )-partition. We now resume our development of the theory of P-partitions. The next lemma will allow us to write any weight enumerator as a sum of weight enumerators of chains.

Download PDF sample

Rated 4.46 of 5 – based on 45 votes