On functions of strengtht

Abstract

For a finite setX, a functionf:P(X) →Z is said to have strengtht if\(\sum\limits_{A\underline{\underline \subset } B} {f(B) = 0} \) for allAP (X), |A|≦t. Supports of functions of strengtht define a matroid onP(X). We study the circuits in this matroid. Some other related problems are also discussed.

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Dedicated to Paul Erdős on his seventieth birthday

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Deza, M., Frankl, P. & Singhi, N.M. On functions of strengtht . Combinatorica 3, 331–339 (1983). https://doi.org/10.1007/BF02579189

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AMS subject classification (1980)

  • 05 B 35