Báo cáo toán học: "Dodgson’s Determinant-Evaluation Rule Proved by" pptx

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 09:46

... A rather more general result of this nature was proved in [3; p. 27, Th. 10.1] to account for certain congruences connected with generalized Frobenius ... [7], [8], [9], J. Ewell [5], L. Winquist [12] and many others (cf., Gupta [10; Sec. 6.3]) have proved partition function congruences based on this idea. In all these theorems, the underlying ... q pn−(p+1)/2 in 1 (q) p−4 ∞ ∞  n=0  2n...

Ngày tải lên: 07/08/2014, 06:22

... patterns can be made with a single motif, following the rules of the game ? In order to try to answer the question, he restricted the rules of choice for the four aspects of the motif that make ... counterclockwise. Figure 1 shows three different motifs that Escher used to generate patterns according to his rules, together with one particular translation block and the patterns generated by th...

Ngày tải lên: 07/08/2014, 06:22

... 2000; Accepted: November 9, 2000 Abstract Recently Zagier proved a remarkable q-series identity. We show that this iden- tity can also be proved by modifying Franklin’s classical proof of Euler’s ... theorem states that (q) ∞ =1+ ∞  r=1 (−1) r (q r(3r−1)/2 + q r(3r+1)/2 ). (1) Recently Zagier proved the following remarkable identity Theorem 1 ∞  n=0 [(q) ∞ − (q) n ]=(q) ∞ ∞  k=1 q k...

Ngày tải lên: 07/08/2014, 06:22

... Eulerian. While few researchers have found an application for Dumont’s statistic since [6], Foata [8] proved the following equidistribution result involving the statistics inv (inversions) and maj (major ... set of linear extensions of P? One might apply another variation of the method above by defining a rule which maps each n-element poset P toasubsetK(P )ofS n which is not a set of line...

Ngày tải lên: 07/08/2014, 06:22

... and only if they are isomorphic by a group automorphism of n . Although this conjecture was disproved by Elspas and Turner three years later [7], the problem and its generalizations have subsequently ... published a conjecture refining the conjecture that had been proposed by ´ Ad´am in 1967 and disproved in 1970. Toida’s conjecture [20] suggests that if  X =  X( n ; S)andifS is a subset of...

Ngày tải lên: 07/08/2014, 07:21

... i − 2) ···3. Before giving the proof of the Theorem 1, we state two lemmas, which can be easily proved by induction on l and j, respectively. Lemma 7. For k − 2 ≥ l ≥ 2, l(k − 2) l−1  i=2 (k ... pairwise disjoint. The direct generalization of the Erd˝os-Ko-Rado theorem for disjoint clouds proved to be false [1]. P. L. Erd˝os and Sz´ekely [6] survey higher order Erd˝os-Ko- Rado theorems

Ngày tải lên: 07/08/2014, 13:21

... possible to construct N ( ¯ G), and then invoke the result of Hagos [6] in the induction step. Hagos proved that the pair (P (G; λ),P( ¯ G; λ)) can be reconstructed from the collection {(P (G−u; λ),P( ¯ G− u; ... induction on k. The base case k = v(G) − 1, which corresponds to the number of spanning trees, was proved in Theorem 3.12. Let the claim be true for all k ∈ [v(G) − 1,q − 1]. To...

Ngày tải lên: 07/08/2014, 13:21

... and only if the q-signed sets corresponding to them are intersecting. Deza and Frankl in 1983 [6] proved that if F is a k- uniform intersecting family in B(n, q), then |F| ≤  n−1 k−1  q k−1 for ... permutations. Sim- ilar results on general colored sets are presented. 1 Introduction Erd˝os, Ko and Rado proved in 1961 [10] that a family of pairwise intersecting k-subsets of an n-set cann...

Ngày tải lên: 07/08/2014, 15:22