Enumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs
نویسندگان
چکیده
منابع مشابه
Enumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs
A Golomb ruler is a sequence of distinct integers (the markings of the ruler) whose pairwise differences are distinct. Golomb rulers, also known as Sidon sets and B2 sets, can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for optimal Golomb rulers (those of minimal length given a fixed number of mark...
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Let G be a finite graph with p vertices and x its chromatic polynomial. A combinatorial interpretation is given to the positive integer (-l)px(-A), where h is a positive integer, in terms of acyclic orientations of G. In particular, (-l)Px(-1) is the number of acyclic orientations of G. An application is given to the enumeration of labeled acyclic digraphs. An algebra of full binomial type, in ...
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The Math Factor podcast posed the problem of finding the smallest number of inch marks on a 12 inch ruler so that one could still measure any integer length from 1 to 12. One needs only four additional marks besides 0 and 12; for example 1, 4, 7, 10 works. This entertaining problem lead to others during the next few minutes (you can listen at mathfactor.uark.edu/2005/10) and inspired us to look...
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A set {ai | 1 ≤ i ≤ k} of non-negative integers is a Golomb ruler if differences ai − aj , for any i 6= j, are all distinct. A set of I disjoint Golomb rulers (DGR) each being a J-subset of {1, 2, · · · , n} is called an (I, J, n) − DGR. Let H(I, J) be the least positive n such that there is an (I, J, n) − DGR. In this paper, we propose a series of conjectures on the constructions and structure...
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II Preface This is a Master's thesis written at the department of Mathematics at the Royal Institute of Technology (KTH) in Stockholm, supervised by Svante Linusson. It is assumed that the reader has studied mathematics at an undergraduate level, and that he is well acquainted with some basic graph theory concepts such as paths and cycles. III Summary This paper is about acyclic orientations of...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2741