Báo cáo toán học: "Descents in Noncrossing Trees " doc

... “generating function”. In Section 2, we find the descent g.f. for noncrossing trees. In Section 3, we show a bijection between noncrossing trees and connected noncrossing graphs that explains combinatorially ... descents. Question 4.3. Find a combinatorial correspondence between noncrossing acyclic basic digraphs and the ascents of noncrossing trees. References [1] L.W.Beine...

Ngày tải lên: 07/08/2014, 07:21

... recursive trees (also called heap ordered trees or non-uniform recursive trees) and binary increasing trees (also called tournament trees) are special instances of simple families of increasing trees. ... equipped with increasing labellings. Thus we are considering simple families of increasing trees, which are introduced in [1]. Several important tree families, in particular re...

Ngày tải lên: 07/08/2014, 13:21

... counting function involved with the two-variable Frobe- nius coin problem when every coin denomination must be used at least once. (In the standard problem it is not obligatory to use every denomination. ... magilatin labellings. In preparation. Available on the Web at www.math.binghamton.edu/zaslav/Tpapers/ [4] ——, An enumerative geometry for magic and magilatin labellings: Computational...

Ngày tải lên: 07/08/2014, 08:22

... singletons, excluding t hose of the form {1}, in all partitions of [n] into k + 1 blocks. Let us show this interesting relation by means of a bijection a s well. We consider set partitions in ... context. Let v mark sin- gleton blocks and u all blocks, then the appropriate bivariate generating function is e u(e x −1−x+vx) . Since the numb er of singleton blocks equal to {1} in partition...

Ngày tải lên: 08/08/2014, 12:22

... H. Prodinger. On the number of descendants and ascendants in random search trees. In preparation, 1996. DESCENDANTS IN HEAP ORDERED TREES OR A TRIUMPH OF COMPUTER ALGEBRA Helmut Prodinger Institut ... journal of combinatorics 3 (1996), #R29 8 6. Binary trees For the sake of completeness and comparison we briefly sketch the corresponding con- siderations for the instance of binary t...

Ngày tải lên: 07/08/2014, 06:20

... journal of combinatorics 10 (2003), #N12 3 Thus we may also think of linear k -trees as maximal linear k-forests or minimally k-connected hypergraphs. 3 All trees are not created equal A linear k-tree ... [5] by imposing a total ordering µ on X, yielding several nice characterizations of k-hypertrees which generalize properties of trees. We show that linear k -trees generalize k-hypertre...

Ngày tải lên: 07/08/2014, 07:21

... therefore inducing an ultrametric tree. Here, T corresponds to certain subtrees of this induced ultrametric tree. the electronic journal of combinatorics 17 (2010), #N6 4 Dissimilarity vectors of trees ... suggestions, including a beautiful simplification of my original proof of Lemma 3.1 and for bringing to my knowledge the paper of Cools [4] and Question 1.2. Thanks to the SFSU-Colombia Co...

Ngày tải lên: 08/08/2014, 01:20

... Finally, in Section 5, based on this study, we give very short proofs of our main results – Theorems 4, 5, 6 and 7. 2 Embedding trees in expanding graphs We start by defining a class of expanding ... almost spanning trees in random graphs, submitted. [4] J. Friedman and N. Pipp enger, Expanding graphs contain all small trees, Combinator- ica 7 (1 987), 71–76. [5] P. Haxell, Tree emb...

Ngày tải lên: 08/08/2014, 11:20

... diabetes [1]. In the field of tissue engineering, magnetic nanoparticles have been previously reported for many applications including cellular labelling, sorting and monitoring, targeted in- vivo ... containing 10% heat inactivated foetal bovine serum [FBS], 2 mM L-glutamine and 1% penicillin streptomycin [Penstrep] (all purchased from Invitrogen Ltd., Renfrew, UK). RAW264.7 cells (ki...

Ngày tải lên: 20/06/2014, 20:20

... cos(0.2πn) 0 0.1 sin(0.2πn) 0 0 0 0 0.01 sin(0.2πn)   , B(n) = (b ij (n)) =   7 + sin(0.2πn) 0.1 sin(0.2πn) 0.01 sin(0.2πn) 0.1 cos(0.2πn) 7 + sin(0.2πn) 0 0.01 sin(0.2πn) 0 7 + sin(0.2π n )   . 11 and (C L u) i (n) ... below). For information about publishing your research in Advances in Difference Equations go to http://www.advancesindifferenceequations.com/authors/instructions/ F...

Ngày tải lên: 20/06/2014, 20:20