The long-line graph of a combinatorial geometry. II: Geometries representable over two fields of different characteristics
type: Item
instance of: scholarly article
title: The long-line graph of a combinatorial geometry. II: Geometries representable over two fields of different characteristics
zbMATH Open document ID: 0645.05026
DOI: 10.1016/0095-8956(90)90095-H
author: Joseph P. S. Kung
published in: Journal of Combinatorial Theory. Series B
publication date: 1990-01-01T00:00:00Z
review text: Let q be a power of a prime and let s be zero or a prime not dividing q. Then the number of points in a combinatorial geometry (or simple matroid of rank n which is representable over GF(q) and a field of characteristic s is at most \((q^{\nu}-q^{\nu -1})\left( \begin{matrix} n+1\\ 2\end{matrix} \right)-n,\) where \(\nu =2^{q-1}-1\). The proof uses the notion of the long-line graph introduced in an earlier paper [Q. J. Math. Oxf., II. Ser. 39, 223-234 (1988)].
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4051648
zbMATH Keywords: combinatorial geometry
zbMATH Keywords: matroid
zbMATH Keywords: growth rates
zbMATH Keywords: representability
zbMATH Keywords: integer matrices
MaRDI profile type: Publication
cites work: A Note on Tutte's Unimodular Representation Theorem
cites work: A class of geometric lattices based on finite groups
cites work: Algebraic characteristic sets of matroids
cites work: On linear systems with integral valued solutions
cites work: Numerically regular hereditary classes of combinatorial geometries
cites work: Combinatorial geometries representable over GF(3) and GF(q). I: The number of points
cites work: THE LONG-LINE GRAPH OF A COMBINATORIAL GEOMETRY. I. EXCLUDING M(K4) AND THE (q + 2)-POINT LINE AS MINORS
cites work: Subspaces with well-scaled frames
cites work: Q3249424
cites work: Q4111952
cites work: Theory of Matroids
full work available at URL: 0095-8956(90)90095-h
OpenAlex ID: W2064283091
description: scientific article; zbMATH DE number 4051648