Matroids from modules

نویسندگان

  • Nils Anders Danielsson
  • Michael B. Smyth
چکیده

The aim of this work is to show that (oriented) matroid methods can be applied to many discrete geometries, namely those based on modules over integral (ordered) domains. The trick is to emulate the structure of a vector space within the module, thereby allowing matroid methods to be used as if the module were a vector space. Only those submodules which are “closed under existing divisors,” and hence behave like vector subspaces, are used as subspaces of the matroid. It is also shown that Hübler’s axiomatic discrete geometry can be characterised in terms of modules over the ring of integers.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Invariants for Polymatroids

Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant G introduced by the first author, are valuative. In this paper we construct the Z-modules of all Z-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the Z-modules of valua...

متن کامل

Structural properties of fuzzy graphs

Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...

متن کامل

Valuative invariants for polymatroids

Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-JiaReiner quasi-symmetric function, and the invariant G introduced by the first author, are valuative. In this paper we construct the Z-modules of all Z-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the Z-modules of valuat...

متن کامل

Homological Properties of Orlik-solomon Algebras

The Orlik-Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E . At first we study homological properties of E-modules as e.g. complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our results to Orlik-Solomon algebras of matroids and give formulas for the complexity, depth and regularity of such...

متن کامل

Latroids and Their Representation by Codes over Modules

It has been known for some time that there is a connection between linear codes over fields and matroids represented over fields. In fact a generator matrix for a linear code over a field is also a representation of a matroid over that field. There are intimately related operations of deletion, contraction, minors and duality on both the code and the matroid. The weight enumerator of the code i...

متن کامل

CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS

The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Electr. Notes Theor. Comput. Sci.

دوره 74  شماره 

صفحات  -

تاریخ انتشار 2002