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2017 | OriginalPaper | Buchkapitel

4. Conditioned Walks

verfasst von : Octavian Iordache

Erschienen in: Implementing Polytope Projects for Smart Systems

Verlag: Springer International Publishing

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Abstract

Conditioned random walks, restricted permutation and self-avoiding walks are studied in this chapter. Construction and deconstruction processes for flexible placements and packing, strategies of interest for very large scales integration and modular constructions are presented Twin trees are described by dual graded graphs. Models for stacking and foldings at different levels of organization are proposed. Algebraic characterizations of self avoiding walks and polygons are introduced. A view of chemical reactions as rewriting rules applied to molecular graphs is sketched.

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Literatur
Zurück zum Zitat Ackerman, E., Barequet, G., Pinter, R.Y.: On the number of rectangular partitions. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete algorithms, pp. 736–745. Society for Industrial and Applied Mathematics (2004) Ackerman, E., Barequet, G., Pinter, R.Y.: On the number of rectangular partitions. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete algorithms, pp. 736–745. Society for Industrial and Applied Mathematics (2004)
Zurück zum Zitat Babson, E., Steingrımsson, E.: Generalized permutation patterns and a classification of the Mahonian statistics. Sém. Lothar. Combin 44(B44b), 547–548 (2000)MathSciNetMATH Babson, E., Steingrımsson, E.: Generalized permutation patterns and a classification of the Mahonian statistics. Sém. Lothar. Combin 44(B44b), 547–548 (2000)MathSciNetMATH
Zurück zum Zitat Beaton, N.R., Flajolet, P., Garoni, T.M., Guttmann, A.J.: Some new self-avoiding walk and polygon models. Fundamenta Informaticae 117(1–4), 19–33 (2012)MathSciNetMATH Beaton, N.R., Flajolet, P., Garoni, T.M., Guttmann, A.J.: Some new self-avoiding walk and polygon models. Fundamenta Informaticae 117(1–4), 19–33 (2012)MathSciNetMATH
Zurück zum Zitat Behr, N., Danos, V., Garnier, I.: Stochastic mechanics of graph rewriting. In: Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2016) Behr, N., Danos, V., Garnier, I.: Stochastic mechanics of graph rewriting. In: Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2016)
Zurück zum Zitat Benkö,G., Flamm, C., Stadler, P.F.: Generic properties of chemical networks: artificial chemistry based on graph rewriting. In: European Conference on Artificial Life 2003, pp. 10–19, Springer, Heidelberg (2003) Benkö,G., Flamm, C., Stadler, P.F.: Generic properties of chemical networks: artificial chemistry based on graph rewriting. In: European Conference on Artificial Life 2003, pp. 10–19, Springer, Heidelberg (2003)
Zurück zum Zitat Bishop, L., Killpatrick, K.: Multi-ordered posets. Elec. J. Comb. Number Theory 7, A06 (2007)MathSciNetMATH Bishop, L., Killpatrick, K.: Multi-ordered posets. Elec. J. Comb. Number Theory 7, A06 (2007)MathSciNetMATH
Zurück zum Zitat Bonichon, N., Bousquet-Mélou, M., Fusy, É.: Baxter permutations and plane bipolar orientations, In: Séminaire Lotharingien de Combinatoire, 61:B61Ah (2010) Bonichon, N., Bousquet-Mélou, M., Fusy, É.: Baxter permutations and plane bipolar orientations, In: Séminaire Lotharingien de Combinatoire, 61:B61Ah (2010)
Zurück zum Zitat Cheung, K.C., Demaine, E.D., Bachrach, J.R., Griffith, S.: Programmable assembly with universally foldable strings (moteins). IEEE Trans. Rob. 27(4), 718–729 (2011)CrossRef Cheung, K.C., Demaine, E.D., Bachrach, J.R., Griffith, S.: Programmable assembly with universally foldable strings (moteins). IEEE Trans. Rob. 27(4), 718–729 (2011)CrossRef
Zurück zum Zitat Di Francesco, P., Golinelli, O., Guitter, E.: Meander, folding, and arch statistics. Math. Comput. Model. 26(8–10), 97–147 (1997a)MathSciNetCrossRefMATH Di Francesco, P., Golinelli, O., Guitter, E.: Meander, folding, and arch statistics. Math. Comput. Model. 26(8–10), 97–147 (1997a)MathSciNetCrossRefMATH
Zurück zum Zitat Di Francesco, P., Golinelli, O., Guitter, E.: Meanders and the Temperley-Lieb algebra. Commun. Math. Phys. 186(1), 1–59 (1997b)MathSciNetCrossRefMATH Di Francesco, P., Golinelli, O., Guitter, E.: Meanders and the Temperley-Lieb algebra. Commun. Math. Phys. 186(1), 1–59 (1997b)MathSciNetCrossRefMATH
Zurück zum Zitat Diaconis, P., Pang, C.A., Ram, A.: Hopf algebras and Markov chains: two examples and a theory. J Algebraic Comb. 39(3), 527–585 (2014)MathSciNetCrossRefMATH Diaconis, P., Pang, C.A., Ram, A.: Hopf algebras and Markov chains: two examples and a theory. J Algebraic Comb. 39(3), 527–585 (2014)MathSciNetCrossRefMATH
Zurück zum Zitat Dulucq, S., Guibert, O.: Stack words, standard tableaux and Baxter permutations. Discrete Mathematics 157(1), 91–106 (1996)MathSciNetCrossRefMATH Dulucq, S., Guibert, O.: Stack words, standard tableaux and Baxter permutations. Discrete Mathematics 157(1), 91–106 (1996)MathSciNetCrossRefMATH
Zurück zum Zitat Giraudo, S.: Algebraic and combinatorial structures on Baxter permutations. Formal Power Ser. Algebraic Comb. FPSAC 23, 387–398 (2011)MathSciNet Giraudo, S.: Algebraic and combinatorial structures on Baxter permutations. Formal Power Ser. Algebraic Comb. FPSAC 23, 387–398 (2011)MathSciNet
Zurück zum Zitat Guttmann, A.J.: Self-avoiding walks and polygons–an overview (2012). (arXiv:1212.3448) Guttmann, A.J.: Self-avoiding walks and polygons–an overview (2012). (arXiv:1212.3448)
Zurück zum Zitat Hulliger, J., Roth, S.W., Quintel, A., Bebie, H.: Polarity of organic supramolecular materials: a tunable crystal property. J. Solid State Chem. 152(1), 49–56 (2000)CrossRef Hulliger, J., Roth, S.W., Quintel, A., Bebie, H.: Polarity of organic supramolecular materials: a tunable crystal property. J. Solid State Chem. 152(1), 49–56 (2000)CrossRef
Zurück zum Zitat Iordache, O.: Polytope projects. Taylor & Francis CRC Press, Boca Raton, FL (2013)CrossRef Iordache, O.: Polytope projects. Taylor & Francis CRC Press, Boca Raton, FL (2013)CrossRef
Zurück zum Zitat Lehn, J-M.: Dynamic combinatorial and virtual combinatorial libraries. Eur. J. Chemistry 5(9):2455–2463 (1999) Lehn, J-M.: Dynamic combinatorial and virtual combinatorial libraries. Eur. J. Chemistry 5(9):2455–2463 (1999)
Zurück zum Zitat Lehn, J.-M.: Toward self-organisation and complex matter. Science 295(29), 2400–2402 (2002)CrossRef Lehn, J.-M.: Toward self-organisation and complex matter. Science 295(29), 2400–2402 (2002)CrossRef
Zurück zum Zitat Nzeutchap, J.: Dual graded graphs and Fomin’s r-correspondences associated to the Hopf algebras of planar binary trees, quasi-symmetric functions and noncommutative symmetric functions, In: International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC, San Diego (2006) Nzeutchap, J.: Dual graded graphs and Fomin’s r-correspondences associated to the Hopf algebras of planar binary trees, quasi-symmetric functions and noncommutative symmetric functions, In: International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC, San Diego (2006)
Zurück zum Zitat Pang, C.Y.: Hopf algebras and Markov chains (2014). (arXiv preprint arXiv:1412.8221) Pang, C.Y.: Hopf algebras and Markov chains (2014). (arXiv preprint arXiv:1412.8221)
Zurück zum Zitat Pham, T.A., Song, F., Alberti, M.N., Nguyen, M.T., Trapp, N., Thilgen, C., Diederich, F., Stöhr, M.: Heat-induced formation of one-dimensional coordination polymers on Au (111): an STM study. Chem. Commun. 51(77), 14473–14476 (2015)CrossRef Pham, T.A., Song, F., Alberti, M.N., Nguyen, M.T., Trapp, N., Thilgen, C., Diederich, F., Stöhr, M.: Heat-induced formation of one-dimensional coordination polymers on Au (111): an STM study. Chem. Commun. 51(77), 14473–14476 (2015)CrossRef
Zurück zum Zitat Shen, Z.C.,Chu, C.C.N.: Bounds on the number of slicing, mosaic, and general floor plans. IEEE Trans. Comput.-Aided Des. Integr. Circuits and Syst. 22(10):1354–1361 (2003) Shen, Z.C.,Chu, C.C.N.: Bounds on the number of slicing, mosaic, and general floor plans. IEEE Trans. Comput.-Aided Des. Integr. Circuits and Syst. 22(10):1354–1361 (2003)
Zurück zum Zitat Shimozono, M., White, D.E.: A color-to-spin domino Schensted algorithm. J. Comb 8(1), R21 (2001)MathSciNetMATH Shimozono, M., White, D.E.: A color-to-spin domino Schensted algorithm. J. Comb 8(1), R21 (2001)MathSciNetMATH
Zurück zum Zitat Sweedler, M.E.: Hopf algebras, Mathematics Lecture Note Series. W. A. Benjamin Inc, New York (1969)MATH Sweedler, M.E.: Hopf algebras, Mathematics Lecture Note Series. W. A. Benjamin Inc, New York (1969)MATH
Zurück zum Zitat Yao, B.: H., Chen, H., Cheng C.K., Graham R.L.: Floor plan representations: Complexity and connections. ACM Transactions on Design Automation of Electronic Systems 8(1), 55–80 (2003)CrossRef Yao, B.: H., Chen, H., Cheng C.K., Graham R.L.: Floor plan representations: Complexity and connections. ACM Transactions on Design Automation of Electronic Systems 8(1), 55–80 (2003)CrossRef
Zurück zum Zitat Young, F.Y., Wong, D.F., Yang, H.H.: Slicing floor plans with boundary constraints. IEEE Trans. Comput.-Aided Des 18, 1385–1389 (1999)CrossRef Young, F.Y., Wong, D.F., Yang, H.H.: Slicing floor plans with boundary constraints. IEEE Trans. Comput.-Aided Des 18, 1385–1389 (1999)CrossRef
Zurück zum Zitat Zhao, Y.: Combinatorial Hopf Algebras On Generating Trees And Certain Generating Graphs. Simon Fraser University, Diss (2014) Zhao, Y.: Combinatorial Hopf Algebras On Generating Trees And Certain Generating Graphs. Simon Fraser University, Diss (2014)
Metadaten
Titel
Conditioned Walks
verfasst von
Octavian Iordache
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-52551-8_4

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