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An exchange theorem for independence structures

Author: C. J. H. McDiarmid
Journal: Proc. Amer. Math. Soc. 47 (1975), 513-514
MSC: Primary 05B35
MathSciNet review: 0363960
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Abstract: I give a simple proof of the following result, which extends a result of C. Greene [1]. Let $ X$ and $ Y$ be sets in an independence structure $ \mathcal{E}$ and let $ X = {X_1} \cup {X_2}$ be a partition of $ X$. Then there exists a partition $ Y = {Y_1} \cup {Y_2}$ of $ Y$ such that for $ i = 1,2,{X_i} \cap {Y_i} = \phi $ and $ {X_i} \cup {Y_i}$ is in $ \mathcal{E}$.

References [Enhancements On Off] (What's this?)

  • [1] C. Greene, A multiple exchange property for bases, Proc. Amer. Math. Soc. 39 (1973), 45-50. MR 47 #56. MR 0311494 (47:56)
  • [2] J. S. Pym and H. Perfect, Submodular functions and independence structures, J. Math. Anal. Appl. 30 (1970), 1-31. MR 41 #8269. MR 0263668 (41:8269)
  • [3] D. R. Woodall, An exchange theorem for bases of matroids, J. Combinatorial Theory 16 (1974), 227-228. MR 0389631 (52:10462)

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