Báo cáo toán học: "A Determinant Identity that Implies Rogers-Ramanujan" docx

... the determinant identity which generalizes a known orthogonal polynomial lemma that implies Theorem 1.1. Section 3 contains some known and some new applications of the 2 × 2 determinant identity. ... 05A30, 33C45 Abstract We give a combinatorial proof of a general determinant identity for associated polynomials. This determinant identity, Theorem 2.2, gives rise to new polyn...

Ngày tải lên: 07/08/2014, 13:21

... introduced a generalization of the Frobenius- Stickelberger determinantal identity involving elliptic functions that generalize the Cauchy determinant. The purpose of this note is to provide a simple ... introduced a generalization of the Frobenius Stickel- berger determinantal identity involving elliptic functions that generalizes the Cauchy determinant. The purpose of this note...

Ngày tải lên: 07/08/2014, 06:20

... of [6]. Let p(m, n; k) denote the probability that, assuming that one has m cards of one colour and n cards of a second colour, with m ≥ n ≥ 0, that one guesses k cards correctly. Sulanke [6], ... colour of the card. We find that there is a slight advantage to playing second in this variation. In what follows, m always refers to number of cards of the colour that is predominant, n to...

Ngày tải lên: 07/08/2014, 06:23

... we can deduce that this maintains the property that in any state (x, y), the probability that the next ball lands in bin 1 is proportional to x p . Specifically, the probability that the minimum ... dx e rg(x) =(1+)  +∞ a h(u 1+ )u  du e rg(u 1+ ) . (15) Equation (8) implies that for all u big enough, h(u 1+ ) ≤ (1 + C)h(u). Moreover, (7) allows us to choose an a such that...

Ngày tải lên: 07/08/2014, 08:20

... 3. Proof. Proposition 3.3 implies a) for n = 1 and Proposition 3.4 implies a) for n ≥ 2, while b) (resp. c)) follows from Proposition 3.6 (resp. Proposition 3.9). Remark. Notice that all the directive ... occurrences of the same letter is always the same, it follows from Hubert [14] that it is a balanced sequence. That is, the letter α is periodically replaced by Pal(23 . . . (k − 1...

Ngày tải lên: 07/08/2014, 15:22

... that induce a nontraceable subdigraph of X. Then these vertices together with any vertex from V (D) − X induce a nontraceable subdigraph of D that is of order 5. It follows from Theorem 5.4 that ... all oriented graphs with the property that every two cycles are vertex disjoint. In particular, it holds for unicyclic oriented graphs. Lemma 4.3 implies that the TC holds (vacuously)...

Ngày tải lên: 07/08/2014, 21:21

... T 2 such that γ(M) ≤ γ(S). Property 2: For any mapping M from T 1 to T 2 there exists a sequence of edit operations such that γ(M)= γ(S). Based on these properties it can be shown that the ... classified for the 10 individuals. Figure 11 shows that the recognition rate may vary markedly depending on the considered global variable and that the highest recognition rate (100%) was ob...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 07/08/2014, 06:22