8,829 research outputs found

    Hypergraph polynomials and the Bernardi process

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    Recently O. Bernardi gave a formula for the Tutte polynomial T(x,y)T(x,y) of a graph, based on spanning trees and activities just like the original definition, but using a fixed ribbon structure to order the set of edges in a different way for each tree. The interior polynomial II is a generalization of T(x,1)T(x,1) to hypergraphs. We supply a Bernardi-type description of II using a ribbon structure on the underlying bipartite graph GG. Our formula works because it is determined by the Ehrhart polynomial of the root polytope of GG in the same way as II is. To prove this we interpret the Bernardi process as a way of dissecting the root polytope into simplices, along with a shelling order. We also show that our generalized Bernardi process gives a common extension of bijections (and their inverses) constructed by Baker and Wang between spanning trees and break divisors.Comment: 46 page

    Chip-firing games on Eulerian digraphs and NP-hardness of computing the rank of a divisor on a graph

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    Baker and Norine introduced a graph-theoretic analogue of the Riemann-Roch theory. A central notion in this theory is the rank of a divisor. In this paper we prove that computing the rank of a divisor on a graph is NP-hard. The determination of the rank of a divisor can be translated to a question about a chip-firing game on the same underlying graph. We prove the NP-hardness of this question by relating chip-firing on directed and undirected graphs

    Chip-firing based methods in the Riemann--Roch theory of directed graphs

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    Baker and Norine proved a Riemann--Roch theorem for divisors on undirected graphs. The notions of graph divisor theory are in duality with the notions of the chip-firing game of Bj\"orner, Lov\'asz and Shor. We use this connection to prove Riemann--Roch-type results on directed graphs. We give a simple proof for a Riemann--Roch inequality on Eulerian directed graphs, improving a result of Amini and Manjunath. We also study possibilities and impossibilities of Riemann--Roch-type equalities in strongly connected digraphs and give examples. We intend to make the connections of this theory to graph theoretic notions more explicit via using the chip-firing framework.Comment: 22 pages, 4 figure

    UNSUR MAGIS DALAM EMPAT ANIME KARYA MIYAZAKI HAYAO PRODUKSI STUDIO GHIBLI 宮崎駿が作った四つのスタジオジブリのアニメにおける魔法の要素

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    ABSTRACT Muriyati, Lilla. 2017. “Magical Element in Four Animes of Miyazaki Hayao by Ghibli Studio”. Undergraduate Thesis. Bachelor Degree of Japanese Literature, Diponegoro University. 1st Advisor Laura Andri R. M, S.S., MA, 2nd Advisor Fajria Noviana, S.S, M.Hum. In this research, the writer decribes about “Magical Element in Four Animes of Miyazaki Hayao by Ghibli Studio”. The writer decided to use this title because anime produced by Ghibli studio are popular with its simple story flow but represent some problems appears in Japanese life society. Moreover, the production of these animation films is absolutely present a real life scene from the society like religious side, legends, myths, also magical event believed by the people. However, often the audience do not really put attention to that and ignore some signs appears in that film so the purpose of this research is to make the audience understand so the message of the films are completely conveyed. The initial step that has been done by the writer was collecting some facts from various resources to be analyzed the characterization and socio-cultural background of the films by using cinematographic theory and trikotomi theory along with triadic triangle from Pierce’s semiotic to classify the appear icon,index and symbol. Some characters and phenomenon appear in thesefour film are representation of icon, index, and also symbols of gods and spirit inspired by Japanese People’s belief. Keyword : Magical, Ghibli, cinematographic, semiotic, triadic

    On the combinatorics of suffix arrays

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    We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of Burrows-Wheeler arrays given in [1], that we apply by reducing suffix sorting to cyclic shift sorting through the use of an additional sentinel symbol. We show that the characterization of suffix arrays for a special case of binary alphabet given in [2] easily follows from our characterization. Based on our results, we also provide simple proofs for the enumeration results for suffix arrays, obtained in [3]. Our approach to characterizing suffix arrays is the first that exploits their relationship with Burrows-Wheeler permutations
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