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Pineapple (Ananas comosus (L.) Merr.) is the most economically valuable crop possessing crassulacean acid metabolism (CAM), a photosynthetic carbon assimilation pathway with high water-use efficiency, and the second most important tropical fruit. We sequenced the genomes of pineapple varieties F153 and MD2 and a wild pineapple relative, Ananas bracteatus(More)
In this paper we study several problems concerning the number of homomorphisms of trees. We begin with an algorithm for the number of homomorphisms from a tree to any graph. By using this algorithm and some transformations on trees, we study various extremal problems about the number of homomorphisms of trees. These applications include a far reaching(More)
The papaya Y-linked region showed clear population structure, resulting in the detection of the ancestral male population that domesticated hermaphrodite papayas were selected from. The same populations were used to study nucleotide diversity and population structure in the X-linked region. Diversity is very low for all genes in the X-linked region in the(More)
The (q, r)-Eulerian polynomials are the (maj−exc, fix, exc) enumerative polynomials of permutations. Using Shareshian and Wachs’ exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical q-Eulerian identities and asked for bijective proofs. We provide such proofs using Foata and Han’s three-variable statistic(More)
We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind JS(n+ k, n; z) by generalizing the analogous results for the Stirling and Legendre-Stirling numbers. More precisely, letting JS(n + k, n; z) = pk,0(n) + pk,1(n)z + · · ·+ pk,k(n)z, we show that (1− t)3k−i+1 ∑ n≥0 pk,i(n)t n is a polynomial in t with nonnegative(More)
Let hom(H,G) denote the number of homomorphisms from a graph H to a graph G. Sidorenko’s conjecture asserts that for any bipartite graph H , and a graph G we have hom(H,G) ≥ v(G) ( hom(K2, G) v(G)2 e(H) , where v(H), v(G) and e(H), e(G) denote the number of vertices and edges of the graph H and G, respectively. In this paper we prove Sidorenko’s conjecture(More)
Let hom(G,H) denote the number of homomorphisms from a graph G to a graph H. In this paper we study the number of homomorphisms of trees into a path, and prove that hom(Pm, Pn) ≤ hom(Tm, Pn) ≤ hom(Sm, Pn), where Tm is any tree on m vertices, and Pm and Sm denote the path and star on m vertices, respectively. This completes the study of extremal problems(More)
Restricted growth functions (RGFs) avoiding the pattern 1212 are in natural bijection with noncrossing partitions. Motivated by recent work of Campbell et al., we study five classical statistics bk, ls, lb, rs and rb on 1212-avoiding RGFs. We show the equidistribution of (ls, rb, lb, bk) and (rb, ls, lb,bk) on 1212-avoiding RGFs by constructing a simple(More)