Fast algorithms for genegrating integer partitions

References

• Akl , S.G. 1981 . A comparison of combination generation methods . ACM Trans, on Math. Software , 7 ( 1 ) : 42 – 45 .
   Web of Science ®Google Scholar
• Akl , S.G. and Stojmenović , I. 1993 . Parallel algorithms for generating integer partitions and compositions . J.of Combinatorial Mathematics and Combinatorial Computing , 13 : 107 – 120 .
   Google Scholar
• Andrews , G.E. 1976 . The theory of partitions , Reading, Ma : Addison-Wesley .
   Google Scholar
• Belbaraka , M. and Stojmenović , I. 1944 . On generating B-trees with constant average delay and in lexicographic order . Information Processing Letters , 49 ( 1 ) : 27 – 32 .
   Web of Science ®Google Scholar
• Berge , C. 1971 . Principles of Combinatorics , Academic Press .
   Google Scholar
• Beyer , T. and Hedetniemi , S.M. 1980 . Constant time generation of rooted trees . SIAM J. Comput. , 9 ( 4 ) : 706 – 712 .
   Web of Science ®Google Scholar
• Dickson , L.E. 1971 . “ History of the theory of numbers ” . In Diophantine Analysis , New York : Chelsea Publishing .
   Google Scholar
• Djokic , B. , Miyakawa , M. , Sekiguchi , S. , Semba , I. and Stojmenović , I. 1989 . A fast algorithm for generating set partitions . The Computer J. , 32 ( 3 ) : 281 – 282 .
   Web of Science ®Google Scholar
• Fenner , T.I. and Loizou , G. 1980 . A binary tree representation and related algorithms for generating integer partitions . The Computer J. , 23 ( 4 ) : 332 – 337 .
   Web of Science ®Google Scholar
• Fenner , T.I. and Loizou , G. 1983 . Tree traversal related algorithms for generating integer partitions . SIAM J. Computing , 12 ( 3 ) : 551 – 564 .
   Web of Science ®Google Scholar
• Fenner , T.I. and Loizou , G. 1981 . An analysis of two related loop-free algorithms for generating integer partitions . Acta Informatica , 16 : 237 – 252 .
   Web of Science ®Google Scholar
• Gupta , U.I. , Lee , D.T. and Wong , C.K. 1983 . Ranking and unranking of B-trees . J. of Algorithms , 4 : 51 – 60 .
   Web of Science ®Google Scholar
• Hardy , G.H. 1918 . Asymptotic formulae in combinatorial analysis . Proc, London Math. Soc. , 17 : 237 – 252 .
   Google Scholar
• Hall , M. 1967 . Combinatorial Theory , Waltham, Mass : Blaisdell .
   Google Scholar
• Hikita , T. 1983 . Listing and counting subtrees of equal size of a binary tree . Inf. Proc. Lett. , 17 : 225 – 229 .
   Web of Science ®Google Scholar
• James , K.R. and Riha , W. 1976 . Algorithm for generating graphs of a given partition . Computing , 16 : 153 – 161 .
   Web of Science ®Google Scholar
• Knuth , D.E. 1968 . “ The Art of Computer Programming ” . In Fundamental Algorithms , Vol. 1 , Reading, Mass : Addison-Wesley .
   Google Scholar
• Lehmer , D.H. 1964 . “ The machine tools of combinatorics ” . In Applied Combinatorial Mathematics , Edited by: Beckenbach , . NY : Wiley .
   Google Scholar
• Liu , C.L. 1968 . Introduction to Combinatorial Mathematics , McGraw Hill .
   Google Scholar
• Mckay , J.K.S. 1965 . Partition generator, Alg, 263 . Comm. ACM , 8 : 493
   Web of Science ®Google Scholar
• McKay , J.K.S. 1965 . Number of restricted partitions of n, Alg. 262 . Comm. ACM , 8 : 493
   Web of Science ®Google Scholar
• Mckay , J.K.S. 1965 . Map of partitions into integers, Alg. 264 . Comm. ACM , 8 : 493
   Web of Science ®Google Scholar
• Mckay , J.K.S. 1970 . Partitions in natural order, Alg. 371 . Comm. ACM , 13 : 52
   Web of Science ®Google Scholar
• Narayana , T.V. , Mathsen , R.M. and Saranji , J. 1971 . An algorithm for generating partitions and its applications . J. Comb. Theory , 11 : 54 – 61 .
   Google Scholar
• Nrjenhius , A. and Wilf , H.S. 1975 . Combinatorial Algorithms , NY : Academic Press .
   Google Scholar
• Nijenhius , A. and Wilf , H.S. 1975 . A method and two algorithms on the theory of partitions . J. Comb. Theory A , 18 : 219 – 222 .
   Web of Science ®Google Scholar
• Page , E.S. and Wilson , L.B. 1979 . An Introduction to Computational Combinatorics , Cambridge Univ. Press .
   Google Scholar
• Read , R.C. 1980 . A survey of graph generation techniques . Lect. Notes in Math. , 884 : 77 – 89 .
   Google Scholar
• Riordan , J. 1958 . An introduction to Combinatorial Analysis , John Wiley .
   Google Scholar
• Reingold , E.M. , Nievergelt , J. and Deo , N. 1977 . Combinatorial Algorithms , Englewood Cliffs, New Jersey : Prentice Hall .
   Google Scholar
• Riha , W. and James , K.R. 1976 . Efficient algorithms for doubly and multiply restricted partitions, Algorithm 29 . Computing , 16 : 163 – 168 .
   Web of Science ®Google Scholar
• Rubin , F. 1976 . Partitions of integers . ACM Transactions on Mathematical Software , 2 ( 4 ) : 364 – 374 .
   Google Scholar
• Ruskey , F. 1978 . Generating t-ary trees lexicographically . SIAM J. Cornput. , 7 : 492 – 509 .
   Web of Science ®Google Scholar
• Sanchis , L. . Counting and generating integer partitions in parallel . Proc. Int. Conf on Computing and Information ICCV92 . pp. 54 – 57 .
   Google Scholar
• Savage , C.D. 1989 . Gray code sequences of partitions . J. of Alg. , 10 : 577 – 595 .
   Web of Science ®Google Scholar
• Sedgewick , R. 1977 . Permutation generation methods . Comp. Surv. , 9 : 137 – 164 .
   Web of Science ®Google Scholar
• Stockmal , F. 1962 . Generation of partitions in part-count form, Algorithm 95 . Comm. ACM , 5 : 344
   Web of Science ®Google Scholar
• Tomasi , C. 1982 . Two simple algorithms for the generation of partitions of an integer . Alta Frequenza, LI , 6 : 352 – 356 .
   Google Scholar
• Van Baronaigien , D.R. 1991 . A loopless algorithm for generating binary tree sequences . Information Processing Letters , 39 : 189 – 194 .
   Web of Science ®Google Scholar
• Wells , M.B. 1971 . Elements of Combinatorial Computing , Oxford : Pergamon Press .
   Google Scholar
• White , J.S. 1970 . Restricted partition generator, Alg. 374 . Comm. ACM , 13 : 120
   Web of Science ®Google Scholar
• White J. S. Number of doubly restricted partitions Alg. 373, ibid.
   Google Scholar
• Zaks , S. and Richards , D. 1979 . Generating trees and other combinatorial objects lexicograpically . SIAM J. on Comput. , 8 ( 1 ) : 73 – 81 .
   Web of Science ®Google Scholar
• Zoghbi , A. 1993 . “ Algorithms for generating integer partitions ” . In M. S, Thesis , University of Ottawa .
   Google Scholar