Báo cáo toán học: "Permutation Tableaux and the Dashed Permutation Pattern 32–1" ppsx

... follows easily from the Erd˝os-Szekeres Theo- rem 2 :theclassAv(B) is finite if and only if B contains both an increasing permutation and a decreasing permutation. The answer to the second question ... gridding of the skew-merged permutation 917456328. and this (increasing) subsequence gives the points in the lower left-hand box of Figure 3. The increasing subsequence...

Ngày tải lên: 07/08/2014, 13:21

... T and the permutation π obtained from T by the first bijection of Corteel and Nadeau, we prove that the inversion number of T equals the number of occurrences of the dashed pattern 32–1 in the ... 0 equals B n . On the other hand, the following relation was proved by Corteel and Nadeau [7]. Theorem 3.2. The number of L-Bell permutation tableaux of length n equ...

Ngày tải lên: 08/08/2014, 14:23

... first kind if and only if L and R are Andr´e permutations of the first kind. Theorem 7. Let π ∈ S n . Then π is an Andr´e permutation of the first kind if and only if it avoids andr ´ e = and . Proof. ... S n avoids the second pattern if and only if π(n) = n. Write π as π = L1R. Then π avoids andr ´ e if and only if L and R avoid the two patterns. Thus the set of all...

Ngày tải lên: 08/08/2014, 14:23

... closed, and convex subsets of the bounded and convex set coC, then µ(C n ) = 0 (n ∈ N), and therefore C ∞ = ∅. Appealing again to the ˇ Smulian theorem [6, Theorem V.6.2] we find that the convex ... denotes the closed and convex hull of A and H(C, D) is the Hausdorff-Pompeiu distance between the bounded subsets C and D of X. The E-L measure of nonconvexity was introdu...

Ngày tải lên: 20/06/2014, 20:20

... are preserved through the mapping, the stable region always lies to the left of the contour. In the v- plane, this is the region above the top horizontal line, and below the lower h orizontal 0 ... Cleveland, OH 44135, USA Authors’ contributions TH and CL worked together in the derivation of the mathematical results. Both authors read and approved the final manuscr...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... Find whether G 1 and G 2 have orthogonal Euler tours. If G 1 and G 2 are equal to the graph G of Problem 1.7 and each directed transition of G has the same colour in G 1 and G 2 , then T 1 and T 2 are ... 2-matroids Let Q 1 and Q 2 be 2-matroids. When Q 1 and Q 2 have the same ground-set and skew classes we shall use Q 1 + Q 2 to denote the parity system which is the...

Ngày tải lên: 07/08/2014, 06:20