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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quotients of tangential $ k$-blocks


Author: Geoffrey Whittle
Journal: Proc. Amer. Math. Soc. 102 (1988), 1088-1098
MSC: Primary 05B35
DOI: https://doi.org/10.1090/S0002-9939-1988-0934895-4
MathSciNet review: 934895
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Abstract: A tangential $ k$-block over $ GF(q)$ is a simple matroid representaba over $ GF(q)$ with critical exponent $ k + 1$ for which every proper loopless minor has critical exponent at most $ k$. Such matroids are of central importance in the critical problem of Crapo and Rota. In this paper we provide sufficient conditions for a quotient of a tangential $ k$-block over $ GF(q)$ to be also a tangential $ k$-block over $ GF(q)$. This enables us to show that there exist rank $ r$ supersolvable tangential $ k$-blocks over $ GF(q)$ exactly when $ {q^k} \geq r \geq k + 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0934895-4
Article copyright: © Copyright 1988 American Mathematical Society