The shuffle pasting, IV

Sjoerd Crans, CTRC Seminar 13 June 2000

This is the fourth in a series of talks investigating the shuffle pasting. The goal is to show that shuffles form a well-formed loop-free pasting scheme, and to characterize well-formed subpasting schemes.

For an n-stage (p,q)-shuffle collection gamma, the following are equivalent:

After recalling the two order relations, I proved (most of) the difficult implication, that fitness implies filling. The crucial thing to show is that if an n-kind is needed for one bounding (n-1)-kind then it is needed for all. In this, a lemma characterizing the <|-order of elements in a filling and fit collection in terms of whether the relevant swap has or has not been carried out in one of them is instrumental.

See sections 8-9 of the paper ``The shuffle pasting'' (in preparation).

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