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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)
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)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. Let hom(G, H) denote the number of homomorphisms from a graph G to(More)