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Almost alternating diagrams and fibered links in S^3
Let be an oriented link with an alternating diagram . It is known that
is a fibered link if and only if the surface obtained by applying
Seifert's algorithm to is a Hopf plumbing. Here, we call a Hopf
plumbing if is obtained by successively plumbing finite number of Hopf
bands to a disk.
In this paper, we discuss its extension so that we show the following
theorem. Let be a Seifert surface obtained by applying Seifert's algorithm
to an almost alternating diagrams. Then is a fiber surface if and only if
is a Hopf plumbing.
We also show that the above theorem can not be extended to 2-almost
alternating diagrams, that is, we give examples of 2-almost alternating
diagrams for knots whose Seifert surface obtained by Seifert's algorithm are
fiber surfaces that are not Hopf plumbing. This is shown by using a criterion
of Melvin-Morton.Comment: 18 pages, 30 figure
Lambda Calculus for Engineers
In pure functional programming it is awkward to use a stateful sub-computation in a predominantly stateless computation. The problem is that the state of the subcomputation has to be passed around using ugly plumbing. Classical examples of the plumbing problem are: providing a supply of fresh names, and providing a supply of random numbers. We propose to use (deterministic) inductive definitions rather than recursion equations as a basic paradigm and show how this makes it easier to add the plumbing
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