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Bijective A-transducers

20th Annual Symposium on Foundations of Computer Science (sfcs 1979), 1979
In this paper we study bijective a-transducers. We derive necessary and sufficient conditions on pairs of regular sets (R,S) such that a bijective a-transducer, mapping R cnto S exists. The results obtained allow the systematic construction of an a-transducer, mapping a set R onto a set S bijectively for surprisingly "different" regular sets R and S.
Hermann A. Maurer, Maurice Nivat
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Differences of Bijections

The American Mathematical Monthly, 2019
When is a function from an abelian group to itself expressible as a difference of two bijections? Answering this question for finite cyclic groups solves a problem about juggling.
Daniel H. Ullman, Daniel J. Velleman
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Bijective projection in a shell

ACM Transactions on Graphics, 2020
We introduce an algorithm to convert a self-intersection free, orientable, and manifold triangle mesh T into a generalized prismatic shell equipped with a bijective projection operator to map T to a class of discrete surfaces contained within the shell whose normals ...
Zhongshi Jiang   +3 more
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Efficient bijective parameterizations

ACM Transactions on Graphics, 2020
We propose a novel method to efficiently compute bijective parameterizations with low distortion on disk topology meshes. Our method relies on a second-order solver. To design an efficient solver, we develop two key techniques. First, we propose a coarse shell to substantially reduce the number of collision constraints that are used to ...
Jian-Ping Su   +3 more
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Permutations and Bijections

2012
Two problems, connected with analysing empirical data are considered. First is a problem of minimizing the number of crossings in a bipartite graph. Second is a pattern matching problem for permutations. In both cases the original problem is transformed into a similar problem for an appropriate mathematical structure, which can be considered as an ...
Leo Vohandu, Ahti Peder, Mati Tombak
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An Extension of Franklin’s Bijection

2001
The author gives a purely combinatorial proof of the identity \[ \prod_{n>m}(1-q^n) = \sum_{n=1}^{\infty} (-1)^n \left[ {n+m \atop m} \right] q^{nm+n(3n+1)/2}(1-q^{2n+m+1}), \] which generalizes Franklin's proof for the case \(m=0\).
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