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"... This is a preprint of an article accepted for publication in Mathematica Slovaca c©2004 (copyright owner as specified in the journal). In a general set-theoretic context, an independent set is defined as a set which avoids certain specified structures called blocks. A formula is given for the number ..."

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This is a preprint of an article accepted for publication in Mathematica Slovaca c©2004 (copyright owner as specified in the journal). In a general set-theoretic context, an independent set is defined as a set which avoids certain specified structures called blocks. A formula is given for the number of independent sets of cardinality k in terms of the numbers of configurations (i.e. non-empty collections) of blocks. AMS classification, primary: 05A19, secondary: 03E05, 05A05, 05B30. This paper is concerned with a formula for counting sets which avoid certain structures. The formula was originally produced in the context of Steiner triple systems [1] but is capable of considerable generalization. The authors believe that the result may be of some wider interest. Accordingly, we here present a version of the result in a more general setting. The proof relies on an application of the inclusion-exclusion principle. 1

### WEAK COLORINGS OF STEINER TRIPLE SYSTEMS

, 2007

"... and have found that it is complete and satisfactory in all respects, Committee Members: Date: and that any and all revisions required by the final examining committee have been made. ..."

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and have found that it is complete and satisfactory in all respects, Committee Members: Date: and that any and all revisions required by the final examining committee have been made.