Recently, Stanley [Longest alternating subsequences of permutations, preprint, arXiv/0511419v1] studied the length of the longest alternating subsequence of a permutation in the symmetric group,where a sequencea, b, c, d, . . . isalternating ifa >bd < · · ·. In this paper, we extend this result to the case of k-ary words. More precisely, we find an explicit formula for the generating functio...

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...

ficus benjamina l. is indoor plant in temperate areas that is a tree species belongs to moraceae family. propagation of this plant is down by vegetative method. this study was conducted to evaluate the effect of iba concentration and time of taking cutting on propagation of ficus benjamina via stenting technique in gorgan university of agricultural sciences and natural resources, in 2012. treat...

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that E [L] /n converges to a constant γk. We prove a conjecture of Sankoff and Mainville from the early 80’s claiming that γk √ k → 2 as k → ∞.

In this paper, we consider the minimization of the longest path length (LPL) for binary decision diagrams (BDDs) and heterogeneous multi-valued decision diagrams (MDDs). Experimental results show that: (1) For many logic functions, node minimization of BDDs also minimizes the LPLs of BDDs. (2) When we use heterogeneous MDDs for representing logic functions and minimize the memory sizes of heter...

For a graphG, let diff(G) = p(G)− c(G), where p(G) and c(G) denote the orders of a longest path and a longest cycle inG, respectively. LetG be a 3-connected graph of order n. In the paper, we give a best-possible lower bound to σ4(G) to assure diff(G) ≤ 1. The result settles a conjecture in J. Graph Theory 37 (2001), 137–156.

A two-rowed array αn = ( a1 a2 . . . an b1 b2 . . . bn ) is said to be in lexicographic order if ak ≤ ak+1 and bk ≤ bk+1 if ak = ak+1. A length ` (strictly) increasing subsequence of αn is a set of indices i1 < i2 < . . . < i` such that bi1 < bi2 < . . . < bi` . We are interested in the statistics of the length of the longest increasing subsequence of αn chosen according to Dn, for distinct fam...

the developing turbulent flow in an open channel is a complex three-dimensional flow influenced by the secondary currents and free surface effects and is, therefore, not amenable to analytical solution. this paper aims to study the impact of three key hydraulic parameters (relative roughness, the froude number and the reynolds number) on the establishment length using computational fluid dynami...