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The independent sets of rank k of a matroid

✍ Scribed by G. Purdy

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
466 KB
Volume
38
Category
Article
ISSN
0012-365X

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✦ Synopsis

We determine the minimum num>er of independent sets of arbitrary fixed rank contained in a matroid M as M varies over all simple (respectively loopless) matroids of fixed rank and cardinality.

πŸ“œ SIMILAR VOLUMES

A polynomial algorithm for constructing
A polynomial algorithm for constructing families of k-independent sets
✍ G. Freiman; E. Lipkin; L. Levitin πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 1003 KB

The present paper describes an algorithm for constructing families of k-independent subsets & of {1,2, . . . , n} with &I >2ck", where c, = d/(k -1)2& and d is a certain constant. The algorithm has a polynomial complexity with respect to the size of the family constructed.

Explicit construction of exponential siz
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Error correcting codes are used to describe explicit collections Fk of subsets of {1, 2,... n}, with IFkl > 2 ckn (ck > 0), such that for any selections A, B of kl and k 2 of members of Fk with kl + k2 = k, there are elements in all the members of A and not in the members of B. This settles a proble

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✍ PΓ©ter L. ErdΕ‘s; Ulrich Faigle; Walter Kern πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 431 KB
Ordering of the elements of a matroid su
Ordering of the elements of a matroid such that its consecutive w elements are independent
✍ Yoji Kajitani; Shuichi Ueno; Hiroshi Miyano πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 480 KB

Let M be a matroid on set E, (El = m, with rank function r. For a positive integer w, M is said to be wth L-ind (C-ind) orderable if there exists an ordering 0 of E such that any consecutive (cyclically consecutive) w elements are independent. ## It is proved that M is wth L-ind orderable if and on