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For a labeled tree on the vertex set {1, 2,. .. , n}, the local direction of each edge (i j) is from i to j if i < j. For a rooted tree, there is also a natural global direction of edges towards the root. The number of edges pointing to a vertex is called its indegree. Thus the local (resp. global) indegree sequence λ = 1 e1 2 e2. .. of a tree on the vertex(More)
BACKGROUND Cells coordinate their metabolism, proliferation, and cellular communication according to environmental cues through signal transduction. Because signal transduction has a primary role in cellular processes, many experimental techniques and approaches have emerged to discover the molecular components and dynamics that are dependent on cellular(More)
A leader of a tree T on [n] is a vertex which has no smaller descendants in T. Gessel and Seo showed that T ∈T n u (# of leaders in T) c (degree of 1 in T) = uP n−1 (1, u, cu), which is a generalization of Cayley's formula, where T n is the set of trees on [n] and P n (a, b, c) = c n−1 i=1 ia + (n − i)b + c. Using a variation of the Prüfer code which is(More)
A further correspondence between (bc, ¯ b)-parking functions and (bc, ¯ b)-forests Abstract. For a fixed sequence of n positive integers (a, ¯ b) := (a, b, b,. .. , b), an (a, ¯ b)-parking function of length n is a sequence (p1, p2,. .. , pn) of positive integers whose nondecreasing rearrangement q1 ≤ q2 ≤ · · · ≤ qn satisfies qi ≤ a + (i − 1)b for any i =(More)
Endometriosis, defined as the presence of endometrial cells outside of the uterine cavity, is a major cause of infertility and pelvic pain, afflicting more than 10% of reproductive age women. Endometriosis is a chronic inflammatory disease and lipopolysaccharide promotes the proliferation and invasion of endometriotic stromal cells. Cysteine-rich secretory(More)