%0 Journal Article %1 gordon83 %A Gordon, Basil %D 1983 %J Journal of Combinatorial Theory, Series A %K combinatorics inclusion-exclusion %N 1 %P 90 - 93 %R 10.1016/0097-3165(83)90043-2 %T Sieve-Equivalence and Explicit Bijections %V 34 %X Suppose A1,…, An are subsets of a finite set A, and B1,…, Bn are subsets of a finite set B. For each subset S of N = 1, 2,…, n, let As = ∩iϵSAi and \BS\ = ∩iϵSBi. It is shown that if explicit bijections fS:AS → \BS\ for each S ⊆ N are given, an explicit bijection h:A-∪i=1Ai→B-∪i=1Bi can be constructed. The map h is independent of any ordering of the elements of A and B, and of the order in which the subsets Ai and Bi are listed.

@article{gordon83, abstract = {Suppose A1,…, An are subsets of a finite set A, and B1,…, Bn are subsets of a finite set B. For each subset S of N = {1, 2,…, n}, let As = ∩iϵSAi and \{BS\} = ∩iϵSBi. It is shown that if explicit bijections fS:AS → \{BS\} for each S ⊆ N are given, an explicit bijection h:A-∪i=1Ai→B-∪i=1Bi can be constructed. The map h is independent of any ordering of the elements of A and B, and of the order in which the subsets Ai and Bi are listed. }, added-at = {2015-07-04T10:44:28.000+0200}, author = {Gordon, Basil}, biburl = {https://www.bibsonomy.org/bibtex/2dc5df36177f78ad542833cdc932f9792/ytyoun}, doi = {10.1016/0097-3165(83)90043-2}, interhash = {0e6c06f6cde6ac601a36cd2e5bef1b5a}, intrahash = {dc5df36177f78ad542833cdc932f9792}, issn = {0097-3165}, journal = {Journal of Combinatorial Theory, Series A }, keywords = {combinatorics inclusion-exclusion}, number = 1, pages = {90 - 93}, timestamp = {2015-10-23T15:20:31.000+0200}, title = {Sieve-Equivalence and Explicit Bijections }, volume = 34, year = 1983 }