Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weak maps of combinatorial geometries


Author: Dean Lucas
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 05B35

Retrieve articles in all journals with MSC: 05B35


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0371693-2
Keywords: Combinatorial geometry, combinatorial pregeometry, weak map, strong map, simple map, binary geometry, Tutte polynomial, matroid, Whitney numbers
Article copyright: © Copyright 1975 American Mathematical Society