(Enter summary)
Abstract: The term combinatorial Gray code was introduced in 1980 to refer to any method for
generating combinatorial objects so that successive objects differ in some pre-specified,
small way. This notion generalizes the classical binary reflected Gray code scheme for
listing n-bit binary numbers so that successive numbers differ in exactly one bit position,
as well as work in the 1960's and 70's on minimal change listings for other combinatorial
families, including permutations and combinations.... (Update)
Cited by: More
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Bent Hamilton Cycles in d-Dimensional Grid Graphs - Ruskey University Of (2003)
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3.7: Hamilton-Connected Derangement Graphs on Sn - David J. Rasmussen, Carla D.. (1994)
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3.0: A Gray Code for Necklaces of Fixed Density - Wang, Savage (1997)
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2.7: Monotone Gray Codes and the Middle Levels Problem - Savage, Winkler (1995)
(Correct)
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- Bette, Ruskey - 1996
9: Pulse code communication (context) - Gray - 1953
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BibTeX entry: (Update)
C. Savage. A survey of combinatorial gray codes. SIAM Review, 39(4):605--629, Dec. 1997. http://citeseer.ist.psu.edu/savage96survey.html More
@article{ savage97survey,
author = "Carla Savage",
title = "A survey of combinatorial {Gray} codes",
journal = "SIAM Review",
volume = "39",
number = "4",
pages = "605--629",
year = "1997",
url = "citeseer.ist.psu.edu/savage96survey.html" }
Citations (may not include all citations):
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48
Group action graphs and parallel architectures (context) - Annexstein, Baumslag et al. - 1990
39
Gray codes and paths on the n-cube (context) - Gilbert - 1958
36
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31
Constructive Combinatorics (context) - Stanton, White - 1986
28
A survey of full length nonlinear shift register cycle algor.. (context) - Fredricksen - 1982
28
A combinatorial problem (context) - de Bruijn - 1946
26
Gray codes for partial match and range queries (context) - Faloutsos - 1988
25
Efficient generation of the binary reflected Gray code (context) - Bitner, Ehrlich et al. - 1976
23
Generating linear extensions fast
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23
Generation of permutations by adjacent transpositions (context) - Johnson - 1963
20
Combinatorial Algorithms for Computers and Calculators (context) - Nijenhuis, Wilf - 1978
18
Gray codes with optimized run lengths (context) - Goddyn, Lawrence et al. - 1988
18
Combinatorial Algorithms: An Update (context) - Wilf - 1989
17
Subcube allocation and task migration in hypercube machines (context) - Chen, Shin - 1990
16
Lexicographic generation of ordered trees (context) - Zaks - 1980
16
Generating binary trees lexicographically (context) - Ruskey, Hu - 1977
16
Permutation generation methods (context) - Sedgewick - 1977
15
Combinatorics for Computer Science (context) - Williamson - 1985
15
An algorithm for generating necklaces of beads in two colors (context) - Fredricksen, Kessler - 1986
14
Generating necklaces
- Ruskey, Savage et al. - 1992
14
Hard enumeration problems in geometry and combinatorics (context) - Linial - 1986
13
ary de Bruijn sequences (context) - Fredricksen, Maiorana et al. - 1978
13
Counting linear extensions is #P-complete (context) - Brightwell, Winkler - 1992
13
Hamiltonian cycles and paths in Cayley graphs and digraphs -.. (context) - Curran, Gallian - 1996
12
On rotations and the generation of binary trees
- Lucas, van Baronaigien et al. - 1993
12
Universal cycles for combinatorial structures (context) - Chung, Diaconis et al. - 1992
11
Gray codes with restricted density (context) - Buck, Wiedemann - 1984
11
Updating the hamiltonian problem - a survey (context) - Gould - 1991
11
Gray code sequences of partitions (context) - Savage - 1989
11
Adjacent interchange generation of combinations (context) - Ruskey - 1988
10
A structured program to generate all topological sorting arr.. (context) - Knuth, Szwarcfiter - 1974
9
Combinatorial Gray codes (context) - Joichi, White et al. - 1980
9
Discrete Mathematics (context) - Ruskey - 1988
9
A technique for generating specialized Gray codes (context) - Vickers, Silverman - 1980
9
Some Hamilton paths and a minimal change algorithm (context) - Eades, Hickey et al. - 1984
9
Generating linear extensions of posets by transpositions
- Ruskey - 1992
8
Generating binary trees by transpositions
- Ruskey, Proskurowski - 1990
8
The antipodal layers problem
- Hurlbert - 1994
8
Hamilton paths in graphs of linear extensions for unions of .. (context) - Stachowiak - 1992
8
The rotation graph of binary trees is hamiltonian (context) - Lucas - 1987
8
Gray codes for reflection groups
- Conway, Sloane et al. - 1989
8
Explicit matchings in the middle levels of the Boolean latti.. (context) - Kierstead, Trotter - 1988
8
Observations on the complexity of generating quasi-gray code.. (context) - Fredman - 1979
8
An algorithm for generating subsets of fixed size with a str.. (context) - Eades, McKay - 1984
7
Efficient Algorithms for Listing Combinatorial Structures (context) - Goldberg - 1993
7
Gray codes from antimatroids
- Pruesse, Ruskey - 1993
7
de Bruijn torus problem
- Hurlbert, Isaak - 1995
7
Curious properties of the Gray code and how it can be used t.. (context) - Gardner - 1972
7
Loopless algorithms for generating permutations (context) - Ehrlich - 1973
6
A campanological problem in group theory (context) - Rankin - 1948
6
Solution of some multi-dimensional lattice path parity diffe.. (context) - Ko, Ruskey - 1988
6
Permutations by interchanges (context) - Heap - 1963
6
A technique for generating Gray codes (context) - Ludman, Sampson - 1981
6
An algorithm to generate all topological sorting arrangement.. (context) - Varol, Rotem - 1981
6
A survey - hamiltonian cycles in Cayley graphs (context) - Witte, Gallian - 1984
6
Construction of uniform Gray codes (context) - Wagner, West - 1991
6
Balanced Gray codes
- Bhat, Savage - 1996
6
Long cycles in vertex-transitive graphs (context) - Babai - 1979
6
A Gray Code for Necklaces of Fixed Density
- Wang - 1994
6
Gray codes for necklaces of fixed density
- Wang, Savage - 1994
5
The shuffle-exchange network has a hamiltonian path
- Feldman, Mysliwietz - 1993
5
Bulletin of the American Mathematical Society (context) - Martin, in - 1934
5
Long cycles in the middle two levels of the Boolean lattice
- Savage - 1993
5
Gray code results for acyclic orientations
- Savage, Squire et al. - 1993
5
A loop-free algorithm for generating the linear extensions o.. (context) - Canfield, Williamson - 1995
5
Generating linear extensions by adjacent transpositions (context) - West - 1993
5
Colorings of diagrams of interval orders and ff-sequences (context) - Felsner, Trotter - 1995
5
the tree graph of a matroid (context) - Holzmann, Harary - 1972
5
Universal Cycles: On Beyond de Bruijn (context) - Hurlbert - 1990
5
Hamilton cycles in regular 2-connected graphs (context) - Jackson - 1980
5
Sequential generation of arrangements by means of a basis of.. (context) - Kompel'makher, Liskovets - 1975
5
The machine tools of combinatorics (context) - Lehmer - 1964
5
Permutation by adjacent interchanges (context) - Lehmer - 1965
5
Gray code generation for MPSK signals (context) - Ludman - 1981
4
Ringing the changes (context) - White - 1983
4
Generating all permutations by graphical transpositions (context) - Slater - 1978
4
A new algorithm for generating necklaces (context) - Wang, Savage - 1990
4
Binary tree Gray codes (context) - Proskurowski, Ruskey - 1985
4
Mathematics Magazine (context) - Metzger - 1985
4
Hamilton cycles which extend transposition matchings in Cayl..
- Ruskey, Savage - 1993
4
Gray codes for randomization procedures (context) - Diaconis, Holmes - 1994
4
A Gray code based ordering for documents on shelves: Classif.. (context) - Losee - 1992
4
Combination generation and Graylex ordering (context) - Chase - 1989
4
Lexicographic matchings cannot form hamiltonian cycles (context) - Duffus, Sands et al. - 1988
4
Combinatorial Generation (context) - Ruskey - 1995
4
IEEE Transactions on Computers (context) - Robinson, Cohn - 1981
4
the generation of all topological sortings (context) - Kalvin, Varol - 1983
4
Mathematics Magazine (context) - Rabinowitz - 1984
4
Digital Communications with Space Applications (context) - Golomb - 1964
3
The search for long paths and cycles in vertex-transitive gr.. (context) - Alspach - 1981
3
A data structure based on Gray code encoding for graphics an.. (context) - Amalraj, Sundararajan et al. - 1990
3
Gray code enumeration of families of integer partitions
- Rasmussen, Savage et al. - 1995
3
Generation of permutations by graphical exchanges (context) - Tchuente - 1982
3
Simple combinatorial Gray codes constructed by reversing sub..
- Ruskey - 1993
3
The prism of the acyclic orientation graph is hamiltonian
- Pruesse, Ruskey - 1995
3
Long cycles in revolving door graphs (context) - Dejter, Quintana - 1987
3
Personal communication (context) - Jacobson, West
3
A Gray code for compositions (context) - Klingsberg - 1982
3
Generating all permutations by graphical derangements (context) - Rall, Slater - 1987
3
Two new Gray codes for acyclic orientations (context) - Squire - 1994
3
Symbolic Gray codes as a data allocation scheme for two disc.. (context) - Chang, Chen et al. - 1992
3
Hamiltonian bipartite graphs (context) - Simpson
3
Data compression and Gray-code sorting (context) - Richards - 1986
3
A Gray code variant: sequencing permutations via fixed point.. (context) - Putnam - 1989
3
Generating binary trees using rotations (context) - Zerling - 1985
3
Origins on the binary code (context) - Heath - 1972
3
Ars Combinatoria (context) - Fan, Fan et al. - 1985
2
Algorithm 382: Combinations of M out of N objects (context) - Chase - 1970
2
Hamilton cycles in the Cayley graph of Sn and a doubly adjac.. (context) - Compton - 1990
2
Generating permutations of a bag by interchanges
- Ko, Ruskey - 1992
2
Combinatorial Gray code and a generalization of the Johnson-.. (context) - Putnam - 1990
2
Information Processing Letters (context) - Kaye, code et al. - 1976
2
Gray codes for A-free strings
- Squire - 1996
2
Electronic mail communication (context) - Moews, Reid
2
Read adjacent interchange combination generation algorithm (context) - Hough, Ruskey et al. - 1988
2
An explicit 1-factorization in the middle of the Boolean lat.. (context) - Duffus, Kierstead et al. - 1994
2
A note on the connectivity of acyclic orientations graphs
- Savage, Zhang - 1995
2
Generation of permutations by transposition (context) - Wells - 1961
2
Generalized Gray codes (context) - Wilf - 1988
2
Hamilton-connected derangement graphs on Sn
- Rasmussen, Savage - 1994
2
Generating permutations with k-differences
- Savage - 1990
2
A binary tree representation and related algorithms for gene.. (context) - Fenner, Loizou - 1980
2
An analysis of two related loop-free algorithms for generati.. (context) - Fenner, Loizou - 1981
1
Hamilton circuits in tree graphs (context) - Cummings - 1966
1
Doubly adjacent Gray codes for the Symmetric group: how to b.. (context) - Compton, Williamson - 1993
1
private communication (context) - Ruskey
1
sequencings of the alternating group (context) - Gould, Roth - 1987
1
The number of linear extensions of subset ordering (context) - Sha, Kleitman - 1987
1
A new method of generating Hamilton cycles on the n-cube (context) - Ramras - 1990
1
Generating neckties: algorithms (context) - Ruskey, Wang - 1994
1
Gray codes for set partitions and restricted growth tails
- Ruskey, Savage - 1994
1
and Fast permutation of the elements of a vector (context) - Boothroyd, the et al. - 1967
1
Computer Bulletin (context) - Boothroyd, PERM - 1965
1
Monotone Gray codes and the middle two levels problem (context) - Savage, Winkler - 1995
1
Toroidal tilings from de Bruijn-good cyclic sequences (context) - Cocke - 1988
1
A Gray code for combinations of a multiset
- Ruskey, Savage - 1995
1
Communications of the ACM (context) - Trotter, Algorithm - 1962
1
Implementation of an algorithm to list Gray code sequences o.. (context) - Beer - 1990
1
Generating the linear extensions of certain posets by adjace.. (context) - Pruesse, Ruskey - 1991
1
A note on Gray codes for neckties (context) - Wang - 1993
1
Ranking and unranking algorithms for trees and other combina.. (context) - Yoshimura - 1987
1
Combinatorial Gray codes and efficient generation (context) - Squire - 1994
1
American Mathematical Monthly (context) - Yoeli, sequences - 1962
1
Note on the generation of rosary permutations (context) - Read - 1972
1
Mathematics Magazine (context) - Eggleton, Wallis et al. - 1985
1
Finding parity difference by involutions
- Stachowiak
1
Generating the acyclic orientations of a graph (context) - Squire - 1994
1
Personal communication (context) - Goddyn, Grozdjak
1
Generating bracelets (context) - Lisonek - 1993
1
Generation of rosary permutations expressed in hamiltonian c.. (context) - Harada - 1971
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/): More
On multi-color partitions and the generalized.. - Jing, Misra, Savage (1999)
(Correct)
On the Multiplicity of Parts in a Random Partition - Corteel, Pittel, al. (1998)
(Correct)
A Lattice Path Approach to Counting Partitions With Minimum Rank - Burstein, Corteel
(Correct)
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