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Efficient reconstruction of partitions
- Source :
-
Discrete Mathematics . Apr2005, Vol. 293 Issue 1-3, p205-211. 7p. - Publication Year :
- 2005
-
Abstract
- Abstract: We consider the problem of reconstructing a partition x of the integer n from the set of its t-subpartitions. These are the partitions of the integer obtained by deleting a total of t from the parts of x in all possible ways. It was shown (in a forthcoming paper) that all partitions of n can be reconstructed from t-subpartitions if n is sufficiently large in relation to t. In this paper we deal with efficient reconstruction, in the following sense: if all partitions of n are -reconstructible, what is the minimum number such that every partition of n can be identified from any distinct subpartitions? We determine the function and describe the corresponding algorithm for reconstruction. Superpartitions may be defined in a similar fashion and we determine also the maximum number of t-superpartitions common to two distinct partitions of n. [Copyright &y& Elsevier]
- Subjects :
- *PARTITIONS (Mathematics)
*NUMBER theory
*ALGORITHMS
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 293
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 17685432
- Full Text :
- https://doi.org/10.1016/j.disc.2004.08.037