Báo cáo toán học: "q, t-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C2)n" doc

... c·ρ ( n 2 ) 1 , the electronic journal of combinatorics 18 (2011), #P158 21 q, t-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C 2 ) n Kyungyong Lee ∗ Department of Mathematics University ... d ′ 2 ), and the x-coordinates of the points in D are non-negative, i.e. D ∈ D. Proof of Claim. We give the exact lower...

Ngày tải lên: 08/08/2014, 14:23

... 306- 791, Korea Full list of author information is available at the end of the article Abstract This paper performs a further investigation on the q-Bernoulli numbers and q- Bernoulli polynomials ... Acikgöz, Erdal and Araci derived some results by using Theorems 1-3. Hence, the other results are incorrect. Now, we redefine the generating function of q-Bernoulli numbers...

Ngày tải lên: 20/06/2014, 22:20

... consequence of Corollary 3. Furthermore, if the multiplicity of 0 as a zero of f is m 0 , then the multiplicity of 0 as a zero of F is also m 0 except m 0 = α = 0; if the multiplicity of −1 as a zero of ... multiplicity of the real zeros of f and F, which generalizes and unifies many known results, including the results of Brenti and Br and en about the q-...

Ngày tải lên: 07/08/2014, 15:23

... choice for the ith team with the probability a i = m i /m,wherem = m 1 + + m N . In the next section, using the generating function for the numbers µ r ,weobtainan expectation of the random variable ... Consider, for example, an Internet voting on the theme: “Which of the N teams will win the world cup?”. If voters don’t know anything about the teams, then they...

Ngày tải lên: 07/08/2014, 07:21

... The circular arrangement problem requires the placement of the vertices of the graph into equidistant positions on a circle of perimeter |V (G)| ,and minimizes the sum of lengths of paths on the ... solved in his thesis the circular arrangement problem for the hypercube, and Bezrukov and Schroeder [1], who showed that for trees the solutions for the li...

Ngày tải lên: 07/08/2014, 08:22

... Mecha- nization of the Ministry of Science and Technology, and the National Science Foundation of China. The second author is partially supported by the EC’s IHRP Program, within the Research Training ... q-identitiesofFuandLascouxprovedbytheq-Rice formula, Quaestiones Math., 27(2004) 391–395. [8] K. Uchimura, An identity for the divisor generating function arising fro...

Ngày tải lên: 07/08/2014, 13:21

... Hence there must beapathoforderk − p + 2 joining x and y in graph G.  Theorem 9 For odd integers k ≥ 5 T  (n, C k )=w(n, k − 1), where k ≤ n ≤ 2k − 2. Proof. The last part of the thesis of Theorem ... b(v)andg(v) we denote the number of red, blue and green edges incident to v, respectively. The degree of vertex v will be denoted by d(v) and the minimum degree of...

Ngày tải lên: 07/08/2014, 13:21

... bits and n output bits, and where the depth of the circuit is in O(log(n)). For a detailed discussion and further survey of this class of problems and their link to communication complexity and ... shows that the information defect of the graphs G ∈ ˜ G n,d (and any shift s of those) is at most n 2 − d 2 . For 1 >  > 0 and for d = n  the graphs...

Ngày tải lên: 07/08/2014, 15:22

... combinatorial proofs of a pair of formulas for P X,Y n,s . First of all, for any set A ⊆ N, let A n = A ∩ [n], and A c n = (A c ) n = [n] − A. Then Hall and R emmel [4] proved the following theorem. Theorem ... before it. So the number of ways to place x i is the difference between the sum of the number of +’s and the number of elements smaller than x i whic...

Ngày tải lên: 08/08/2014, 01:20

... new iteration, called the SP-iteration, and they proved the Mann, Ishikawa, Noor and SP- iterations are equivalent and the SP-iteration converges faster than the others for the class of continuous and nondecreasing ... U and by using (3.5) and mathematical 21 comparison of the rate of convergence. The first one was introduced by Berinde [27]. He used this idea...

Ngày tải lên: 20/06/2014, 20:20