D-finite symmetric functions by Mariolys Rivas

By Mariolys Rivas

Show description

Read or Download D-finite symmetric functions PDF

Similar algebra & trigonometry books

Inequalities: a Mathematical Olympiad approach

This booklet is meant for the Mathematical Olympiad scholars who desire to organize for the examine of inequalities, a subject now of common use at numerous degrees of mathematical competitions. during this quantity we current either vintage inequalities and the extra helpful inequalities for confronting and fixing optimization difficulties.

Trends in commutative algebra

This e-book relies on lectures through six the world over recognized specialists provided on the 2002 MSRI introductory workshop on commutative algebra. They concentrate on the interplay of commutative algebra with different components of arithmetic, together with algebraic geometry, crew cohomology and illustration thought, and combinatorics, with all precious historical past supplied.

Schaum's Outline of Mathematical Handbook of Formulas and Tables, 3ed (Schaum's Outline Series)

Schaum's has happy scholars for fifty Years. Now Schaum's largest are in New versions! For part a century, greater than forty million scholars have depended on Schaum's to aid them examine quicker, research larger, and get best grades. Now Schaum's celebrates its fiftieth birthday with a brand-new glance, a brand new layout with 1000's of perform difficulties, and entirely up to date info to comply to the newest advancements in each box of research.

Recent Developments in the Inverse Galois Problem: A Joint Summer Research Conference on Recent Developments in the Inverse Galols Problem July 17-23, ... Seattle

This booklet includes the refereed court cases of the AMS-IMS-SIAM Joint summer time examine convention on contemporary advancements within the Inverse Galois challenge, held in July 1993 on the college of Washington, Seattle. a brand new evaluate of Serre's subject matters in Galois concept serves as a kick off point. The e-book describes the most recent learn on specific presentation of absolutely the Galois crew of the rationals.

Extra resources for D-finite symmetric functions

Example text

2. There exists another argument based on singularity analysis to prove that a function is not D-finite. 3 (Folklore). The number of partitions of n, denoted by p(n), is not P-recursive. In order to prove this, it suffices to show that the ordinary generating series ∑ ∏ 1 p(n)tn = 1 − tk n≥0 k is not D-finite. For this, notice that such generating function has an infinite number of singularities, which is not possible for a D-finite power series. We do not cover this type of analysis in our work, the reader is directed to Flajolet and Sedgewick [6] for further details.

Recall that two bases {uλ } and {vλ } are said to be adjoint if ⟨uλ , vµ ⟩ = δλµ for all partitions λ and µ. CHAPTER 6. 5. 5, ( Dpλ (pk )Dpµ (pk ) λ,µ = h(t) ∑ Dpλ (pk )Dpλ (pk ) λ ( pλ ∗ pµ zλ zµ ) pλ zλ = h(t) Dp(0) (pk )Dp(0) (pk )p(0) + Dpk (pk )Dpk (pk ) pk ) k = h(t)(p2k + kpk ). Denote by Λ∗ the algebra of symmetric power series. The map ⟨⟨⟩⟩ : Λ → Λ∗ given by ∑ ⟨⟨sλ ⟩⟩ = n sλ[n] , is called the reduced notation for sλ , which can be extended by linearity, since the Schur functions form a basis of Λ.

Then, Kµ1 the number of standard Young tableaux of shape µ is equal to n Kµ1 = ∏ n! , x∈T hook(x) n where Kµ1 is the Kostka number of shape µ and type 1n . This formula has been proven in many different ways, from both algebraic and combinatorial points of view. We direct the reader to the recent proof [2] by Bandlow. 3. Denote by am the number of standard Young tableaux of shape (m−|λ|, λ), for a fixed partition λ. Then {am }m≥0 is P-recursive. Proof. Using the hook formula we get: am = = ∏ m! x∈T(m−|λ|,λ) hook(x) m!

Download PDF sample

Rated 4.59 of 5 – based on 3 votes