The shuffle pasting, II

Sjoerd Crans, CTRC Seminar 18 April 2000

This is the second 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.

I first recalled a bit from last week's talk, for the benefit of people who didn't attend that talk and as a refresher for the others. Then, I showed that the pasting scheme whose cells are n-dimensional (p,q)-shuffles has no direct loops, and I introduced a rank function, which basically measures how far 0's are from being up front and 1's are from being down rear, with a twist to take into account the places and the parity of the swaps. Eventually, I will use induction over the rank in proofs of well-formedness statements.

See sections 4-5 of the paper ``The shuffle pasting'' (in preparation).

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