Integer complexity and well-ordering
نویسندگان
چکیده
منابع مشابه
Integer Complexity, Addition Chains, and Well-Ordering
In this dissertation we consider two notions of the “complexity” of a natural number, the first being addition chain length, and the second known simply as “integer complexity”. The integer complexity of n, denoted ‖n‖, is the smallest number of 1’s needed to write n using an arbitrary combination of addition and multiplication. It is known that ‖n‖ ≥ 3 log3 n for all n. We consider the differe...
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Let % be a class of graphs and let i be the subgraph or the induced subgraph relation. We call % an idea/ (with respect to I) if G I G' E % implies that G E %. In this paper, we study the ideals that are well-quasiordered by I. The following are our main results. If 5 is the subgraph relation, we characterize the well-quasi-ordered ideals in terms of excluding subgraphs. If I is the induced sub...
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Robertson and Seymour (1990) proved that graphs of bounded tree-width are well-quasi-ordered by the graph minor relation. By extending their arguments, Geelen, Gerards, and Whittle (2002) proved that binary matroids of bounded branch-width are well-quasi-ordered by the matroid minor relation. We prove another theorem of this kind in terms of rank-width and vertex-minors. For a graph G = (V,E) a...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2015
ISSN: 0026-2285
DOI: 10.1307/mmj/1441116656