Báo cáo toán học: "Bijective Proofs of Identities from Colored Binary Trees" doc

... certain class of binary trees and the set of colored 5-ary trees. The generalization of the parity reversing involution and the bijection to forests of colored binary trees and forests of colored 5-ary ... improper binary tree, then let φ(F ) be the forest of colored binary trees obtained from F by changing B k to φ(B k ). From Theorem 2.1, we see φ(F) is an im...

Ngày tải lên: 07/08/2014, 15:22

... r.The components of λ are called the parts of λ. The integer n, the sum of all the parts of λ, is called the norm of λ and is denoted by n(λ). The (ordinary) Ferrers diagram of λ is an array of cells ... q-analogue of the hook formula (see the Theorem in section 4) which all the other proofs do not. Secondly, the same idea also works to provide a bijective proof of the hoo...

Ngày tải lên: 07/08/2014, 06:20

... Howe- Umeda-Kostant-Sahi identities immediately imply, and were inspired by, identities of Cayley (see [T1]), Garding [G], and Shimura [S], respectively. In this paper, we give short combinatorial proofs of Capelli’s ... anti-symmetric analog of Capelli’s identity. Although we, at present, are unable to give a combinatorial proof similar to the above proofs, we state this identit...

Ngày tải lên: 07/08/2014, 06:20

... construction and give a bijective proof using inclusion–exclusion. 2 Exposition of identities and proofs The origin of this paper was the attempt to give a bijective proof of the following identity for ... 6 Proof of the Pl¨ucker relations In order to show that the general assertions of Section 5 do in fact lead to some inter- esting identities, we give a proof of the Pl¨ucke...

Ngày tải lên: 07/08/2014, 06:22

... there are a variety of combinatorial or bijective proofs. Rather than attempt any classification of the various bijective proofs, we refer the reader to Pak’s excellent survey [21] of bijective methods, ... bijective part of the hybrid proofs given in the paper, we have used only the simplest of a ll bijections, namely, conjugation. It is likely that other bijections will lead to...

Ngày tải lên: 08/08/2014, 14:22

... and full text (HTML) versions will be made available soon. New proofs of Schur-concavity for a class of symmetric functions Journal of Inequalities and Applications 2012, 2012:12 doi:10.1186/1029-242X-2012-12 Huan-Nan ... (1 − t)y j . Proof. (i) Directly calculating yields f  (t) = m  j=1 (x j − y j )  1 tx j + (1 − t)y j − 1 1 + tx j + (1 − t)y j  NEW PROOFS OF SCHUR-CONCAVIT...

Ngày tải lên: 20/06/2014, 21:20

... parenthesis-shuffle of size n a pair consisting of a tree of size n and a binary tree of size n + 1. The remarks above should convince the reader that the mapping Λ is a bijection between these two sets of objects. 4.2 ... t k respectively. the electronic journal of combinatorics 14 (2007), #R9 26 The rest of this section is devoted to the proof of Theorem 1. We first give a ch...

Ngày tải lên: 07/08/2014, 15:22

Ngày tải lên: 05/08/2014, 15:20

... actually is a solution of the bibasic hypergeometric telescoping problem (1). This completes the proof of the correctness of Algorithm Telescope p,q . the electronic journal of combinatorics 3 (1996), ... out that most of the bibasic hypergeometric summation identities from literature can be proved and even found this way. A Mathematica implementation of the algorithm is avail...

Ngày tải lên: 07/08/2014, 06:20

... present an algebraic proof of a result with the same flavour as the latter: T n+2 (1, −1) = T n (2, −1), where T n (1, −1) has the combinatorial interpretation of being the number of 0–1–2 increasing ... function of parking functions or the inversion enumerator of labelled trees on n vertices, see [10]. In the following section we prove the main theorem of the paper: ∗ Supported by...

Ngày tải lên: 07/08/2014, 15:22