Monotone Gray codes and the middle levels problem
نویسندگان
چکیده
منابع مشابه
Monotone Gray Codes and the Middle Levels Problem
An n-bit binary Gray code is an enumeration of all n-bit binary strings so that successive elements differ in exactly one bit position; equivalently, a hamilton path in the Hasse diagram of Bn (the partially ordered set of subsets of an n-element set, ordered by inclusion.) We construct, for each n, a hamilton path in Bn with the following additional property: edges between levels i− 1 and i of...
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For any integer n ≥ 1 a middle levels Gray code is a cyclic listing of all bitstrings of length 2n+1 that have either n or n+1 entries equal to 1 such that any two consecutive bitstrings in the list differ in exactly one bit. The question whether such a Gray code exists for every n ≥ 1 has been the subject of intensive research during the last 30 years, and has been answered affirmatively only ...
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For any integer n ≥ 1 a middle levels Gray code is a cyclic listing of all nelement and (n+ 1)-element subsets of {1, 2, . . . , 2n+ 1} such that any two consecutive subsets differ in adding or removing a single element. The question whether such a Gray code exists for any n ≥ 1 has been the subject of intensive research during the last 30 years, and has been answered affirmatively only recentl...
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In this paper we introduce a natural mathematical structure derived from Samuel Beckett’s play “Quad”. We call this structure a binary Beckett-Gray code. We enumerate all codes for n ≤ 6 and give examples for n = 7, 8. Beckett-Gray codes can be realized as successive states of a queue data structure. We show that the binary reflected Gray code can be realized as successive states of two stack d...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1995
ISSN: 0097-3165
DOI: 10.1016/0097-3165(95)90091-8