Báo cáo toán học: "Enumeration of Restricted Permutation Triples" pps

... (11) 3 Enumeration of m-tuples of Permutations More generally, we may consider the m-tuples of permutations of S n with exactly k occurrences of “ R m ”. Denote by D(n, k) the number of such multiple ... electronic journal of combinatorics 17 (2010), #R131 6 Enumeration of Restricted Permutation Triples Xiaojing Chen School of Mathematics and Computational Science China...

Ngày tải lên: 08/08/2014, 12:22

... number of tilings of half of a hexagon or half of a diamond, with dents at given places. This is not new: see [7] and [8]. 2. Express the number of tilings of the figure as a whole as a sum of squares ... transpose, then the determinant of MM t is equal to the sum of the squares of the k by k minors of M. The number of tilings of a (k, q, k) hexagon in which the indic...

Ngày tải lên: 07/08/2014, 06:20

... Proof of Theorem 7.1. Ignoring the case with only o ne block of odd length, fix a choice of s elements from [a + 1,n] to be placed in the first two blocks. We have shown that more of these permutations ... joint distribution of descent and major index over restricted sets of permutations. Annals of C o mbinatorics. to a ppear. [5] Jacques D´esarm´enien and Michelle L. Wachs. Des...

Ngày tải lên: 07/08/2014, 21:21

... Enumeration of perfect matchings of Q m,n,r 3.1 The sign of pfB(x 1 , x 2 ) In order to decide the sign of pfaffians of B(x 1 , x 2 )(x 1 , x 2 = ±1), we distinguish the perfect matchings of Q m,n,r into ... Proc. 1997 Symposium on the Theory of Computing (STO C). [16] H. Narumi and H. Hosoya, Proof of the generalized expressions of the number of perfect matchings of polyc...

Ngày tải lên: 08/08/2014, 12:22

... number of −1 entries (to the number of orbits of −1 entries in the case of symmetric ASM’s). For a generic value of the g lobal parameter a, when we put all variables to 1, the weight of zero ... is no QTASM of size 4N + 2. Proof. Let us suppose that M is a QTASM of even size 2L. Now we use the fact that the size of an ASM is given by the sum of its entries, and the symmet...

Ngày tải lên: 08/08/2014, 12:22

... key role as simple permutations. Some examples of an algorithmic use of the substitution decomposition of permutations ar e the computation of the set of common intervals of two (or more) permutations ... pin -permutation. Indeed, all permutations of size at most 5 are pin-permutations. Figure 17 The permutatio n 15243, which is the starting point for t he construction of ever...

Ngày tải lên: 08/08/2014, 14:22

... hyperoperations that associate with two elements of H not an element, as in a classical structure, but a subset of H. One of the interests of the researchers in the field of hyperstructur es is to construct ... Let V n be the number of non isomorphic Varlet hyper groups of order n. Then, V n+m ≥ V n V m , for all n, m ∈ N. Using the results of [22] we can enumerat e the number...

Ngày tải lên: 08/08/2014, 14:23

... the end of the first row, κ 2 cells are deleted from the end of the second row, etc. Letting N be the size of (n m ) \ κ, a SYT of truncated shape (n m ) \ κ is a labeling of the cells of this shape ... partitions as sets, [m] is the disjoint union of the shape of T 1 and the the shape of T 2 . Proof. (i) is clear. In order to prove (ii), denote the shifted shapes of T 1 an...

Ngày tải lên: 08/08/2014, 14:23

... one left extension step of type L on x k in X; R k : taking one right extension step of type R on x k in X; LC k : cutting one letter on the left of x k in X by an action of type LC k ; RC k : ... [6]. Vietnam Journal of Mathematics 34:4 (2006) 459–472 Generating of Minimal Unavoidable Sets Phan Trung Huy and Nguyen Thi Thanh Huyen Department of Math., Hanoi University of Tech...

Ngày tải lên: 06/08/2014, 05:20

... expressed as a rational linear combination of products of single and double Euler sums of weight n. We define the weight of a product of Euler sums as the sum of the arguments appearing in the product. ... combination of products of double and single Euler sums. The proof involves finding and solving linear equations which relate the different types of sums to each other. We al...

Ngày tải lên: 07/08/2014, 06:20