40,241 research outputs found

    A Natural Bijection between Permutations and a Family of Descending Plane Partitions

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    We construct a direct natural bijection between descending plane partitions without any special part and permutations. The directness is in the sense that the bijection avoids any reference to nonintersecting lattice paths. The advantage of the bijection is that it provides an interpretation for the seemingly long list of conditions needed to define descending plane partitions. Unfortunately, the bijection does not relate the number of parts of the descending plane partition with the number of inversions of the permutation as one might have expected from the conjecture of Mills, Robbins and Rumsey, although there is a simple expression for the number of inversions of a permutation in terms of the corresponding descending plane partition.Comment: 10 pages, title "modestified", unnecessary definitions removed, remarks shortene

    On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain

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    A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical application we show that periodic kink solutions (kink chains) of the double sine-Gordon model can be described in a canonical form in terms of generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table

    Inversion variants in human and primate genomes

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    For many years, inversions have been proposed to be a direct driving force in speciation since they suppress recombination when heterozygous. Inversions are the most common large-scale differences among humans and great apes. Nevertheless, they represent large events easily distinguishable by classical cytogenetics, whose resolution, however, is limited. Here, we performed a genome-wide comparison between human, great ape, and macaque genomes using the net alignments for the most recent releases of genome assemblies. We identified a total of 156 putative inversions, between 103 kb and 91 Mb, corresponding to 136 human loci. Combining literature, sequence, and experimental analyses, we analyzed 109 of these loci and found 67 regions inverted in one or multiple primates, including 28 newly identified inversions. These events overlap with 81 human genes at their breakpoints, and seven correspond to sites of recurrent rearrangements associated with human disease. This work doubles the number of validated primate inversions larger than 100 kb, beyond what was previously documented. We identified 74 sites of errors, where the sequence has been assembled in the wrong orientation, in the reference genomes analyzed. Our data serve two purposes: First, we generated a map of evolutionary inversions in these genomes representing a resource for interrogating differences among these species at a functional level; second, we provide a list of misassembled regions in these primate genomes, involving over 300 Mb of DNA and 1978 human genes. Accurately annotating these regions in the genome references has immediate applications for evolutionary and biomedical studies on primates

    Shellsort with three increments

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    A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments (h,g,1)(h,g,1). In particular, when h=Θ(n7/15)h=\Theta(n^{7/15}) and g=Θ(h1/5)g=\Theta(h^{1/5}), the average running time is O(n23/15)O(n^{23/15}). The proof involves interesting properties of the inversions in random permutations that have been hh-sorted and gg-sorted

    Do Some Stakeholders in Publicly Traded Firms Benefit at the Expense of Others as a Result of Corporate Inversions?

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    This report examines corporate inversions to determine whether this practice benefits the majority of stakeholders or merely a select few. A sample of firms previously incorporated in the United States that have since undergone inversions is examined to answer this question. Annual stock price returns, stock price volatility, and earnings per share changes from the sample of inversion firms are the main sources of data examined. These results are compared to the S&P 500 and peer firms to determine whether the changes can be attributed to the inversions, or are merely a result of general economic conditions. Supporting topics addressed in this paper include an overview of legislation related to inversions and suggestions to mitigate the negative consequences of inversions. This study shows that there are no observable benefits to shareholder wealth arising from corporate inversions. While there were changes in the data from pre to post inversion, they were not unique to the inversion firms as the same changes were observed in the peer firms. However, the study showed that there is a fundamental difference between inversion firms when compared to the S&P 500
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