Geodesic
Weakly prudent self-avoiding bridges
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

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We define and enumerate a new class of self-avoiding walks on the square lattice, which we call <i>weakly prudent bridges</i>. Their definition is inspired by two previously-considered classes of self-avoiding walks, and can be viewed as a combination of those two models. We consider several methods for recursively generating these objects, each with its own advantages and disadvantages, and use these methods to solve the generating function, obtain very long series, and randomly generate walks of arbitrary size. We find that the growth constant of these walks is approximately 2.58, which is larger than that of any previously-solved class of self-avoiding walks. 
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     author = {Bacher, Axel and Beaton, Nicholas},
     title = {Weakly prudent self-avoiding bridges},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2445},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2445/}
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Bacher, Axel; Beaton, Nicholas. Weakly prudent self-avoiding bridges. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2445. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2445/

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