Báo cáo toán học: "Records in set partitions" doc

... 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 ... remain unchanged. This mapping is an involution on the set of partitions of [n] and thus it is a bijection. For example, 1|234 → 1|234, 12|34 → 1|2|34 and 123|4 → 14|2|3. Comparing the genera...

Ngày tải lên: 08/08/2014, 12:22

... s tudy of minimally intersecting set partitions, we investi- gate minimally intersecting set partitions of type B. Our main result is a formula for the number of m inimally intersecting r-tuples ... combinatorics 17 (2010), #R22 10 Minimally Intersecting Set Partitions of Type B Willia m Y.C. Chen and David G.L. Wang Center for Combin atorics, LPMC-TJKL C Nankai University, Tianjin, P.R...

Ngày tải lên: 08/08/2014, 11:20

... every two connected set partitions σ 1 , σ 2 in the subgraphs G 1 X , G 2 X inducing β in X, constitute a connected set partition σ = σ 1 ⊔σ 2 in G X that induces β in X satisfying {G[σ]} = {G 1 [σ 1 ]}⊔{G 2 [σ 2 ]}, ... X) is a splitting of G. The set X is a separating vertex set of G. Let X ⊆ V , then Π c (G, β) for β ∈ Π(X) denotes the set of connected set partitions of...

Ngày tải lên: 08/08/2014, 12:23

... “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 ... 05A15 Abstract The generating function for descents in noncrossing trees is found. A bijection shows combinatorially why the descent generating function with descents set equal...

Ngày tải lên: 07/08/2014, 07:21

... 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

... trees are equipped with increasing labellings. Thus we are considering simple families of increasing trees,which are introduced in [1]. Several important tree families, in particular recursive ... of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i. e. labellings of the nodes by distinct int...

Ngày tải lên: 07/08/2014, 13:21

... decreasing chain if for every i ∈ [t − 1] the column containing c i is to left of the column containing c i+1 and the row containing c i is above the row of c i+1 . An increasing chain is defined ... useful in our study of pattern-avoidance, and we prove our key results. We begin by introducing a general relationship between pattern-avoidance in partitions and pattern-avoidance in filling...

Ngày tải lên: 07/08/2014, 15:23

... we know to be sets of word (k−1 )-recurrence for all k are IP sets. (An IP set in N consists of an in nite sequence (x i ) and it s finite sums formed by adding terms with distinct indices, i. e.   i∈α x i : ... in w. The latter function is continuous in t he variables f λ and subject to the constraint  λ f λ = 1 its minimum value of k M−J obtains at f λ = 1 k for all λ (a calculus...

Ngày tải lên: 08/08/2014, 14:23

... 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