New PDF release: D-finite symmetric functions

By Mariolys Rivas

Show description

Read Online or Download D-finite symmetric functions PDF

Similar algebra & trigonometry books

Solving Word Problems - download pdf or read online

Scholars in the course of the international worry and dread fixing notice difficulties. As scholars’ studying talents have declined, so have their skills to unravel be aware difficulties. This ebook deals suggestions to the main common and non-standard observe difficulties on hand. It follows the feedback of the nationwide Council of lecturers of arithmetic (NCTM) and comprises the categories of difficulties frequently chanced on on standardized math checks (PSAT, SAT, and others).

Download e-book for iPad: Beyond Formulas in Mathematics and Teaching: Dynamics of the by Daniel Chazan

Explores the most important dynamics of training - developing who one's scholars are, what to educate and the way to have interaction with dynamic personalities. The e-book examines intimately a teacher's evolving understandings in their scholars, algebra and teachers-student lecture room roles.

Algebra für Höhlenmenschen und andere Anfänger: Eine - download pdf or read online

Wissen Sie schon alles über Zahlen? Es gibt gerade, krumme, gebrochene, aber wie viele? Und rechnen Sie immer richtig? Eine jährliche Inflationsrate von three Prozent ergibt nach 20 Jahren eine Preissteigerung von 60 Prozent – oder sind es seventy five Prozent? Schon Ihre Vorfahren vor 10. 000 Jahren hatten bereits das Denken gelernt.

Y. Yoshino's Cohen Macaulay modules over Cohen Macaulay rings PDF

The aim of those notes is to give an explanation for intimately a few subject matters at the intersection of commutative algebra, illustration conception and singularity thought. they're in line with lectures given in Tokyo, but in addition comprise new examine. it's the first cohesive account of the realm and should supply an invaluable synthesis of contemporary study for algebraists.

Additional resources for D-finite symmetric functions

Example text

1 λ C k,l = (l − k + m + 1) for k > m + 1. 2 1 (l + k − m + 2) for m ≥ k − 1. 2 Algorithm. Algorithm. 1: Coefficients for two-row shape Schur functions Some work has been done to characterize the coefficients that appear in the Kronecker product of reduced Schur functions indexed by two-row partitions. 3 (Two-row shape partitions, Scharf, Thibon and Wybourne [20]). For k ≥ l fixed: sk[n] ∗ sl[n] = ∑ λ C k, l sλ[n] = λ p l ∑ ∑ sk−p sl−p sp−q . p=0 q=0 Scharf, Thibon and Wybourne gave explicit formulas and algorithms to calculate the coefficients that appear in this case by noticing that λ can have at most three rows, which results from the Littlewood-Richardson multiplication rule of Schur functions.

Two years later this concept was generalized to the multivariate case by Zeilberger [25]. And after ten years, Gessel [7] developed a D-finiteness theory for symmetric series. In this chapter we recall all these definitions and some important results concerning the closure properties of D-finiteness with respect to scalar and inner products. 1 Definitions Consider any field Q with characteristic 0 and Q[[x]] the ring of formal power series in x. We say that a power series F ∈ Q[[x]] is D-finite (differentiably finite) in a variable x if F and all of its derivatives F (n) = dn F dxn (n ≥ 1) span a finite-dimensional vector subspace of Q[[x]] over the field Q(x) of rational functions.

2. If n = 10, then s4 + s4,2,1 = s6,5 + s2,4,3,1 , where (6, 5) is a partition, but (2, 4, 3, 1) is not. By applying the Jacobi-Trudi identity we obtain that s2,4,2,1 = −s3,3,3,1 . Thus s4 + s4,2,1 = s6,5 − s3,3,3,1 . Littlewood found the following general formula for the Kronecker product of two reduced Schur functions. CHAPTER 6. 2 (Littlewood[13]). For two fixed partitions λ, µ with |λ| = |µ| and a fixed nonnegative integer n ≥ 0: sλ[n] ∗ sµ[n] = ∑ sλ/αγ sµ/βγ (sα ∗ sβ ). α,β,γ where αγ = (α1 + γ1 , α2 + γ2 , .

Download PDF sample

D-finite symmetric functions by Mariolys Rivas

by Robert

Rated 4.01 of 5 – based on 31 votes