Recently Richard Stanley [3] initiated a study of the distribution of the length asn(w) of the longest alternating subsequence in a random permutation w from the symmetric group Sn. Among other things he found an explicit formula for the generating function (on n and k) for Pr (asn(w) ≤ k) and conjectured that the distribution, suitably centered and normalized, tended to a Gaussian with varianc...

The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group Sn has been the object of much investigation. We develop comparable results for the length as(w) of the longest alternating subsequence of w, where a sequence a, b, c, d, . . . is alternating if a > b < c > d < · · · . For instance, the expected value (mean) of as(w) for w ∈ Sn is exactly (4n + 1)/6...

We consider the problem of finding a long, simple path in an undirected graph. We present a polynomial-time algorithm that finds a path of length Ω ( (logL/ log logL)2 ) , where L denotes the length of the longest simple path in the graph. This establishes the performance ratio O ( n(log logn/ logn)2 ) for the longest path problem, where n denotes the number of vertices in the graph.

onion is one of the important strategic crop plants of a highly valuable nutritional food source, consumed almost around the whole world. thus, the genetically oriented studies around the plant are valuable and inevitable. for a following of these studies, some onion masses from various regions throughout iran, including: kashan-white, azarshahr-red, isfahan-dorcheh, ghom-white, zanjan-gholighe...

Let S = s1, s2, . . . , sn be an integer sequence. The longest increasing subsequence problem is to find an increasing subsequence of S with the longest length. By regarding S as a weight sequence of the vertices in a path, we can redefine the longest increasing subsequence problem on graphs as follows. Let G = (V,E) be a graph in which every vertex v ∈ V has a weight w(v). A longest increasing...

this study was conducted to investigate some aspects of the reproductive system of exopalaemon styliferus (h. milne edwards, 1840) population in downstream bahmanshir river during summer, 2008. a total of 472 specimens collected from sampling site?? stations, males and females comprised 55.4% and 43.6%, respectively (14.4% ovigerous female and 30.1% non-ovigerous females). the minimum size of m...

A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete multipartite digraph. L. Volkmann (1998) raised the following question: Let D be a strong semicomplete multipartite digraph with a longest path of length l. Does there exist a strong spanning oriented subgraph of D with a lo...

This study was carried out to compare the histomorphological structures of oviductal regions of the apparently healthy adult laying hens (Gallus gallus dometicus) and ducks (Ansa ansa domesticus). For this purpose, 20 hens and 20 female ducks aged between 1–1.5 years were used. After euthanasia, the oviducts were dissected out and all of the gross morphometrical parameters including length, wid...