821 research outputs found
Real fields and repeated radical extensions
The main result of this paper is that if E is a field extension of finite odd
degree over a real field Q, and if E is a repeated radical extension of Q, then
every intermediate field is also a repeated radical extension of Q. This paper
also contains a number of other results about repeated radical extensions
Simple formulas for lattice paths avoiding certain periodic staircase boundaries
There is a strikingly simple classical formula for the number of lattice
paths avoiding the line x = ky when k is a positive integer. We show that the
natural generalization of this simple formula continues to hold when the line x
= ky is replaced by certain periodic staircase boundaries--but only under
special conditions. The simple formula fails in general, and it remains an open
question to what extent our results can be further generalized.Comment: Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new
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