An exchange theorem for independence structures
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- by C. J. H. McDiarmid PDF
- Proc. Amer. Math. Soc. 47 (1975), 513-514 Request permission
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
- Curtis Greene, A multiple exchange property for bases, Proc. Amer. Math. Soc. 39 (1973), 45–50. MR 311494, DOI 10.1090/S0002-9939-1973-0311494-8
- J. S. Pym and Hazel Perfect, Submodular functions and independence structures, J. Math. Anal. Appl. 30 (1970), 1–31. MR 263668, DOI 10.1016/0022-247X(70)90180-0
- D. R. Woodall, An exchange theorem for bases of matroids, J. Combinatorial Theory Ser. B 16 (1974), 227–228. MR 389631, DOI 10.1016/0095-8956(74)90067-7
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 513-514
- MSC: Primary 05B35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0363960-9
- MathSciNet review: 0363960