Báo cáo toán học: "P´lya’s Permanent Problem o" ppsx

... alt =""

Ngày tải lên: 05/08/2014, 09:46

... class="bi x0 y1 w2 h 2" alt =""

Ngày tải lên: 05/08/2014, 09:46

... alt =""

Ngày tải lên: 05/08/2014, 09:46

... class="bi x0 y0 w1 h 1" alt =""

Ngày tải lên: 05/08/2014, 10:20

... class="bi x0 y0 w1 h 1" alt =""

Ngày tải lên: 05/08/2014, 10:20

... the Chinese Remainder Theorem, a proof of which was published by Aviezri early in his career [5]. A major problem in molecular biology is to determine the mechanism of protein folding. In water, ... Aviezri, shaking his head sadly, “I expected something like this would happen. Everyone is driving the electronic journal of combinatorics 8 (no. 2) (2001), #I3 2 Aviezri Fraenkel’s work...

Ngày tải lên: 07/08/2014, 06:23

... x]showsthats λ [s (1 a ,b) ][1 − x] = 0 unless λ is a hook. So we have shown that s [s à ]| hooks = 0 unless both and à are hooks, proving statement 1. If we now let λ =(1 c ,d), and for the ... is odd So statement 1 follows immediately by conjugating statement 1 of Theorem 4.5. When a is even, statement 6 follows by conjugating the formula in statement 6 of Theorem 4.5 and then subst...

Ngày tải lên: 07/08/2014, 08:20

... the permanent of a matrix, and this is P´olya’s permanent problem. 4 A complexity class consisting of hard counting problems. Counting the number of Hamiltonian cycles of a graph is another problem ... (2004), #R79 40 3 Origins In this section we discuss four origins of P´olya’s permanent problem. Permanents The permanent and determinant of an n ì n matrix A =[a ij ]aregivenby...

Ngày tải lên: 07/08/2014, 08:22

... journal of combinat orics 11(2) (2005), #R21 10 P -partitions and a multi-parameter Klyachko idempotent Peter McNamara Instituto Superior T´ecnico Departamento de Matem´atica Avenida Rovisco Pais 1049-001 ... definition naturally makes the Klyachko idem- potent appealing to combinatorialists and, for example, [2, 4, 11, 15] study the Klyachko idempotent and its generaliza...

Ngày tải lên: 07/08/2014, 08:22

... Ap´ery’s Double Sum is Plain Sailing Indeed Carsten Schneider ∗ Research Institute for Symbolic Computation J. Kepler University Linz A-4040 Linz, Austria Carsten.Schneider@risc.uni-linz.ac.at Submitted: ... Symbolic summation assists combinatorics. S´em. Lothar. Combin., 56:1–36, 2007. Article B56b. [7] K. Wegschaider. Computer generated proofs of binomial multi -sum identities....

Ngày tải lên: 07/08/2014, 13:21

... u(n). Theorem 3.2 The partition function t(n) is equal to the number of partitions of n with an even number of even hooks, and the partition function u(n) is equal to the number of partitions of n ... for all partitions of n + 1. Let λ be a partition of n + 1 a nd v = (i, j) be any inner corner of the Young diagram of λ, that is, the removal of the square v gives a Young diagram of a p...

Ngày tải lên: 08/08/2014, 11:20

... Classifications: 05A15, 05A19 Abstract Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han’s formulas has been generalized to k-ary trees by Yang. ... staircase labeling. 1 Introduction Motivated by the hook length formula of Postnikov [6], Han [4] discovered two hook length formulas for binary trees. Han’s...

Ngày tải lên: 08/08/2014, 14:23

... the main theorem. Proof of Theorem 4.1. If m = 0, then the theorem reduces to the q-Dyson Theorem. So we assume that m  1. Applying Theorem 2 .3 to the constant term in the left-hand side of (4.6) ... (2.7) The idea to prove this theorem is by iterating Lemma 2.2 to transform the random i 1 in (2.6 ) to zero and then a pplying Theorem 2.1. But in the proof there are many te...

Ngày tải lên: 08/08/2014, 14:23

... 7 On Rowland’s sequence Fernando Chamizo, Dulcinea Raboso and Seraf´ın Ruiz-Cabello ∗ Department of Mathematics Universidad Aut´onoma de Madrid 28049 Madrid. Spain fernando. chamizo@uam.es dulcinea. raboso@ uam.es serafin.ruiz@uam.es Submitted: ... =  j<n (p j − 1) and S(1) = 0. The following is a characterization of Rowland’s chains. Proposition 3.3 A finite sequenc...

Ngày tải lên: 08/08/2014, 14:23

... r ed ucing a constant term in 2k variables to a constant term in k variables. As applications, Zeilberger’s constant terms are converted to single determinants. The result extends for two classes ... Jacobi’s Change of Variable Formula We first complete the proof of Identity 2 by transforming the constant term into known constant terms. Here, we mean Macdonald’s constant...

Ngày tải lên: 08/08/2014, 14:23