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Abstract: A necklace is an equivalence class of binary strings under rotation. In this paper, we present a Gray code listing of all n-bit necklaces with d ones so that (i) each necklace is listed exactly once by a representative from its equivalence class and (ii) successive representatives, including the last and the first in the list, differ only by the transposition of two bits. The total time required is O(nN (n; d)), where N (n; d) denotes the number of n-bit binary necklaces with d ones. This is... (Update)
Context of citations to this paper: More
...for constructing a Gray code for necklaces of fixed density. The procedure has been implemented in C and is included in the appendix to [Wan]. A subsequent modification requires storage only O(n) In this section, we show the time required is O(nN(n; d) where N(n; d) is the...
.... intricate construction, how to construct a Gray code in which successive necklace representatives differ only by the swap of a 0 and a 1 [Wan94, WS94] (Figure 11. It remains open whether necklaces with a fixed number of 1 s can be generated in constant amortized time, either by...
Cited by: More
An Efficient Algorithm for Generating Necklaces with Fixed.. - Ruskey, Sawada (1999) (Correct)
A Survey of Combinatorial Gray Codes - Savage (1996) (Correct)
A Gray Code for Necklaces of Fixed Density - Wang, Savage (1997) (Correct)
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1.0: Gray Code Enumeration of Families of Integer Partitions - Rasmussen, West, Savage (Correct)
0.9: Generating Necklaces - Ruskey, Savage, Wang (1992) (Correct)
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6: An algorithm for generating necklaces of beads in two colors (context) - Fredricksen, Kessler - 1986
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BibTeX entry: (Update)
T.M.Y Wang and C.D. Savage, A Gray code for necklaces of fixed density, SIAM J. Discrete Math, 9 (1996) 654-673. http://citeseer.ist.psu.edu/wang97gray.html More
@article{ wang96gray,
author = "Terry Min Yih Wang and Carla D. Savage",
title = "A Gray Code for Necklaces of Fixed Density",
journal = "SIAM Journal on Discrete Mathematics",
volume = "9",
number = "4",
pages = "654-673",
year = "1996",
url = "citeseer.ist.psu.edu/wang97gray.html" }
Citations (may not include all citations):23 Generating linear extensions fast - Pruesse, Ruskey
23 Generation of permutations by adjacent transpositions (context) - Johnson - 1963
20 Combinatorial Algorithms for Computers and Calculators (context) - Nijenhuis, Wilf - 1978
18 Combinatorial Algorithms: An Update (context) - Wilf - 1989
15 An algorithm for generating necklaces of beads in two colors (context) - Fredricksen, Kessler - 1986
14 Generating necklaces - Ruskey, Savage et al. - 1992
12 On rotations and the generation of binary trees - Lucas, van Baronaigien et al. - 1993
11 Gray codes with restricted density (context) - Buck, Wiedemann - 1984
11 Gray code sequences of partitions (context) - Savage - 1989
11 Adjacent interchange generation of combinations (context) - Ruskey - 1988
9 PERM (Algorithm 115 (context) - Trotter - 1962
9 Generating the linear extensions of certain posets by transp.. (context) - Pruesse, Ruskey - 1991
9 Generating linear extensions of posets by transpositions - Ruskey - 1992
8 Generating binary trees by transpositions - Ruskey, Proskurowski - 1990
8 The rotation graph of binary trees is hamiltonian (context) - Lucas - 1987
8 Hamilton paths in graphs of linear extensions for unions of .. (context) - Stachowiak - 1992
7 The curious properties of the Gray code and how it can be us.. (context) - Gardner - 1972
6 Gray codes for necklaces of fixed density - Wang - 1994
5 Generating linear extensions by adjacent transpositions (context) - West - 1993
4 A Gray code for set partitions (context) - Kaye - 1976
4 A new algorithm for generating necklaces (context) - Wang, Savage - 1990
4 Necklaces of beads in k colors and k-ary de Bruijn sequences (context) - Fredricksen, Maiorana - 1978
3 Symbolic Gray code as a perfect multiattribute hashing schem.. (context) - Chang, Lee et al. - 1982
3 Fast canonization of circular strings (context) - Shiloach - 1981
3 Data compression and Gray-code sorting (context) - Richards - 1986
3 A Gray code for compositions (context) - Klingsberg - 1982
3 Symbolic Gray code as a data allocation scheme for two-disc .. (context) - Chang, Chen et al. - 1992
1 Gray Codes for Families of Integer Partitions (context) - Rasmussen, Savage et al.
1 A Gray code based ordering for documents on shelves (context) - Losee - 1992
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.csc.ncsu.edu/faculty/savage/papers.html): More
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Monotone Gray Codes and the Middle Levels Problem - Savage, Winkler (1995) (Correct)
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