## Weak maps of combinatorial geometries

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- by Dean Lucas PDF
- Trans. Amer. Math. Soc.
**206**(1975), 247-279 Request permission

## Abstract:

Weak maps of combinatorial geometries are studied, with particular emphasis on rank preserving weak bijections. Equivalent conditions for maps to be reversed under duality are given. It is shown that each simple image (on the same rank) of a binary geometry $G$ is of the form $G/F \oplus F$ for some subgeometry $F$ of $G$. The behavior of invariants under mappings is studied. The Tutte polynomial, Whitney numbers of both kinds, and the Möbius function are shown to behave systematically under rank preserving weak maps. A weak map lattice is presented and, through it, the lattices of elementary images and preimages of a fixed geometry are studied.## References

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## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**206**(1975), 247-279 - MSC: Primary 05B35
- DOI: https://doi.org/10.1090/S0002-9947-1975-0371693-2
- MathSciNet review: 0371693