P. Klingsberg. A Gray code for compositions. Journal of Algorithms, 3:41--44, 1982. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
A Survey of Combinatorial Gray Codes - Savage (1996) (23 citations) (Correct)
....1 7 7 4 2 1 2 1 17 8 4 5 4 2 1 Figure 8: Gray codes for various families of integer partitions generate the k compositions of n so that each is obtained from its predecessor by moving one ball from its box to another. Knuth solved this in 1974 while reading the galleys of the book and in [Kli82], Klingsberg gives a CAT implementation of Knuth s Gray code. Combinations and compositions can be simultaneously generalized as follows. Let C(s; m 1 ; m t ) denote the set of all ordered t tuples (x 1 ; x t ) satisfying x 1 : x t = s and 0 x i m i for i = 1; t. If ....
P. Klingsberg. A Gray code for compositions. Journal of Algorithms, 3:41--44, 1982.
A Gray Code for Necklaces of Fixed Density - Wang, Savage (1997) (4 citations) (Correct)
.... problems have been solved and the complexities of the solutions to other problems have been improved [Gar, ChLeDu, ChChCh, Los, Ric] There are many examples of combinatorial families for which Gray codes are known, including permutations [Joh, Tro] combinations [BuWi, NiWi, Rus1] compositions [Kli], set partitions [Kay] integer partitions [Sav, RaSaWe] binary trees [RuPr, Luc, LuRoRu] and linear extensions [PrRu1, PrRu2, Rus2, Sta, Wes] When an application requires an exhaustive examination of all objects in a combinatorial family, Gray codes can be used to speed up the task. With a ....
P. Klingsberg, "A Gray code for compositions," Journal of Algorithms 3, (1982) 41-44. 29
Gray Codes for Reflection Groups - Conway, Sloane, Wilks (1989) (8 citations) (Correct)
....of permutations were given by Johnson [32] and Trotter [53] in the early 1960 s. Other Hamiltonian circuits through all n permutations (satisfying different constraints) arise in bell ringing ( 49] 57] 60] Although several other generalizations of Gray codes have appeared ( 3] 22] 33] [37], 42] 48] 52] we believe our version is new. The theorem is proved in 2, and 3 gives some examples. In particular we give specific Gray codes for all the examples ( 1 , 2 , 3 , 2 , 3 , 2 , 3 , 2 (m) in dimensions n 3. It is worth remarking that not all Cayley diagrams ....
P. Klingsberg, A Gray code for compositions, J. Algorithms, 3 (1982), 41-44.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC