Zigzag Stacks and m-Regular Linear Stacks

@article{Chen2014ZigzagSA,
  title={Zigzag Stacks and m-Regular Linear Stacks},
  author={William Y. C. Chen and Qianghui Guo and Lisa Hui Sun and Jian Wang},
  journal={Journal of computational biology : a journal of computational molecular cell biology},
  year={2014},
  volume={21 12},
  pages={
          915-35
        }
}
The contact map of a protein fold is a graph that represents the patterns of contacts in the fold. It is known that the contact map can be decomposed into stacks and queues. RNA secondary structures are special stacks in which the degree of each vertex is at most one and each arc has length of at least two. Waterman and Smith derived a formula for the number of RNA secondary structures of length n with exactly k arcs. Höner zu Siederdissen et al. developed a folding algorithm for extended RNA… 
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Background Citations
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Methods Citations
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5 Citations

Enumeration of Extended m-Regular Linear Stacks

The study of extended [Formula: see text]-regular linear stacks, in which the degree of each terminal point is bounded by 3, is led to, which is closed to real protein contact maps.

Combinatorics of Contacts in Protein Contact Maps

The generating function for m-regular linear stacks is modified by introducing a new variable y regarding to the number of arcs and an equation satisfied by the generating function is derived of the overallNumber of arcs in m- regular linear stacks with n vertices and k arcs.

Regular Simple Queues of Protein Contact Maps

2-regular and 3-regular simple queues, for which the degree of each vertex is at most one and the arc lengths are at least 2 and 3, respectively, are concerned, and a recurrence relation for the generating function of Motzkin paths with $$k_i$$ki peaks at level i is derived.

On the Number of Saturated and Optimal Extended 2-Regular Simple Stacks in the Nussinov-Jacobson Energy Model

It is known that both RNA secondary structure and protein contact map can be presented using combinatorial diagrams, the combinatorial enumeration and related problems of which have been studied…

A bijective method for saturated extended 2-regular simple stacks in the Nussinov-Jacobson energy model

This paper constructs a bijection between the saturated extended 2 -regular simple stacks and the forests of small trees, which are rooted trees with height one and also called meadows in graph theory.

References

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