Rank functions of strict cg-matroids
نویسنده
چکیده
A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by S. Fujishige, G. A. Koshevoy, and Y. Sano in [9]. A cg-matroid whose rank function is naturally defined is called a strict cg-matroid. In this paper, we give characterizations of strict cg-matroids by their rank functions.
منابع مشابه
Matroids on convex geometries (cg-matroids)
We consider matroidal structures on convex geometries, which we call cg-matroids. The concept of a cg-matroid is closely related to but different from that of a supermatroid introduced by Dunstan, Ingleton, and Welsh in 1972. Distributive supermatroids or poset matroids are supermatroids defined on distributive lattices or sets of order ideals of posets. The class of cg-matroids includes distri...
متن کاملThe greedy algorithm for strict cg-matroids
A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by S. Fujishige, G. A. Koshevoy, and Y. Sano in [6]. Strict cg-matroids are the special subclass of cg-matroids. In this paper, we show that the greedy algorithm works for strict cg-matroids with natural weightings, and also show that the greedy algorithm works for a hereditary system on a convex geometry wit...
متن کاملOn the rank functions of H-matroids
The notion of H-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of H-matroids by the greedy algorithm. In this note, we give a characterization of some H-matroids by rank functions. 2010 MSC: 05B35, 90C27
متن کاملA Generalisation of the Matroid Lift Construction
This paper introduces a general matroid-theoretic construction which includes, as special cases, elementary lifts of matroids and bias matroids of biased graphs. To perform the construction on a matroid A/ , it is necessary (but not sufficient) to have a submodular function inducing M . Elementary lifts are obtained when the submodular function chosen is the rank function of M . We define what ...
متن کاملA matroid-friendly basis for the quasisymmetric functions
A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the quasisymmetric functions associated to matroids by the Hopf algebra morphism F of Billera, Jia, and Reiner [3]. In particular, for loopless matroids, this basis reflects the grading by matroid rank, as wel...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008