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On the Markov-Dyck shifts of vertex type
1. | Department of Mathematics, Joetsu University of Education, Joetsu 943-8512 |
References:
[1] |
M.-P. Béal, M. Blockelet and C. Dima, Sofic-Dick shifts,, preprint, ().
|
[2] |
A. Costa and B. Steinberg, A categorical invariant of flow equivalence of shifts, Ergodic Theory and Dynamical Systems, 74 (2014), 44pp, arXiv:1304.3487.
doi: 10.1017/etds.2014.74. |
[3] |
J. Cuntz, Simple $C^*$-algebras generated by isometries, Commun. Math. Phys., 57 (1977), 173-185.
doi: 10.1007/BF01625776. |
[4] |
J. Cuntz and W. Krieger, A class of $C^*$-algebras and topological Markov chains, Inventions Math., 56 (1980), 251-268.
doi: 10.1007/BF01390048. |
[5] |
E. Deutsch, Dyck path enumeration, Discrete Math., 204 (1999), 167-202.
doi: 10.1016/S0012-365X(98)00371-9. |
[6] |
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley, New York, 1983. |
[7] |
T. Hamachi, K. Inoue and W. Krieger, Subsystems of finite type and semigroup invariants of subshifts, J. Reine Angew. Math., 632 (2009), 37-61.
doi: 10.1515/CRELLE.2009.049. |
[8] |
T. Hamachi and W. Krieger, A construction of subshifts and a class of semigroups,, preprint, ().
|
[9] |
F. Harry, Line graphs, in Graph Theory, Massachusetts, Addison-Wesley, (1972), 71-83. |
[10] |
G. Keller, Circular codes, loop counting, and zeta-functions, J. Combinatorial Theory, 56 (1991), 75-83.
doi: 10.1016/0097-3165(91)90023-A. |
[11] |
B. P. Kitchens, Symbolic Dynamics, Springer-Verlag, Berlin, Heidelberg and New York, 1998.
doi: 10.1007/978-3-642-58822-8. |
[12] |
W. Krieger, On the uniqueness of the equilibrium state, Math. Systems Theory, 8 (1974), 97-104.
doi: 10.1007/BF01762180. |
[13] |
W. Krieger, On a syntactically defined invariant of symbolic dynamics, Ergodic Theory Dynam. Systems, 20 (2000), 501-516.
doi: 10.1017/S0143385700000249. |
[14] |
W. Krieger, On subshifts and semigroups, Bull. London Math., 38 (2006), 617-624.
doi: 10.1112/S0024609306018625. |
[15] |
W. Krieger and K. Matsumoto, Zeta functions and topological entropy of the Markov Dyck shifts, Münster J. Math., 4 (2011), 171-183. |
[16] |
W. Krieger and K. Matsumoto, Markov-Dyck shifts, neutral periodic points and topological conjugacy (tentative title),, in preparation., ().
|
[17] |
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511626302. |
[18] |
K. Matsumoto, Cuntz-Krieger algebras and a generalization of Catalan numbers, Int. J. Math., 24 (2013), 1350040, 31pp.
doi: 10.1142/S0129167X13500407. |
[19] |
K. Matsumoto, $C^*$-algebras arising from Dyck systems of topological Markov chains, Math. Scand., 109 (2011), 31-54. |
[20] |
R. P. Stanley, Enumerative Combinatrics I, Wadsworth & Brooks/Cole Advanced Books, Monterey, CA, 1986.
doi: 10.1007/978-1-4615-9763-6. |
show all references
References:
[1] |
M.-P. Béal, M. Blockelet and C. Dima, Sofic-Dick shifts,, preprint, ().
|
[2] |
A. Costa and B. Steinberg, A categorical invariant of flow equivalence of shifts, Ergodic Theory and Dynamical Systems, 74 (2014), 44pp, arXiv:1304.3487.
doi: 10.1017/etds.2014.74. |
[3] |
J. Cuntz, Simple $C^*$-algebras generated by isometries, Commun. Math. Phys., 57 (1977), 173-185.
doi: 10.1007/BF01625776. |
[4] |
J. Cuntz and W. Krieger, A class of $C^*$-algebras and topological Markov chains, Inventions Math., 56 (1980), 251-268.
doi: 10.1007/BF01390048. |
[5] |
E. Deutsch, Dyck path enumeration, Discrete Math., 204 (1999), 167-202.
doi: 10.1016/S0012-365X(98)00371-9. |
[6] |
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley, New York, 1983. |
[7] |
T. Hamachi, K. Inoue and W. Krieger, Subsystems of finite type and semigroup invariants of subshifts, J. Reine Angew. Math., 632 (2009), 37-61.
doi: 10.1515/CRELLE.2009.049. |
[8] |
T. Hamachi and W. Krieger, A construction of subshifts and a class of semigroups,, preprint, ().
|
[9] |
F. Harry, Line graphs, in Graph Theory, Massachusetts, Addison-Wesley, (1972), 71-83. |
[10] |
G. Keller, Circular codes, loop counting, and zeta-functions, J. Combinatorial Theory, 56 (1991), 75-83.
doi: 10.1016/0097-3165(91)90023-A. |
[11] |
B. P. Kitchens, Symbolic Dynamics, Springer-Verlag, Berlin, Heidelberg and New York, 1998.
doi: 10.1007/978-3-642-58822-8. |
[12] |
W. Krieger, On the uniqueness of the equilibrium state, Math. Systems Theory, 8 (1974), 97-104.
doi: 10.1007/BF01762180. |
[13] |
W. Krieger, On a syntactically defined invariant of symbolic dynamics, Ergodic Theory Dynam. Systems, 20 (2000), 501-516.
doi: 10.1017/S0143385700000249. |
[14] |
W. Krieger, On subshifts and semigroups, Bull. London Math., 38 (2006), 617-624.
doi: 10.1112/S0024609306018625. |
[15] |
W. Krieger and K. Matsumoto, Zeta functions and topological entropy of the Markov Dyck shifts, Münster J. Math., 4 (2011), 171-183. |
[16] |
W. Krieger and K. Matsumoto, Markov-Dyck shifts, neutral periodic points and topological conjugacy (tentative title),, in preparation., ().
|
[17] |
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511626302. |
[18] |
K. Matsumoto, Cuntz-Krieger algebras and a generalization of Catalan numbers, Int. J. Math., 24 (2013), 1350040, 31pp.
doi: 10.1142/S0129167X13500407. |
[19] |
K. Matsumoto, $C^*$-algebras arising from Dyck systems of topological Markov chains, Math. Scand., 109 (2011), 31-54. |
[20] |
R. P. Stanley, Enumerative Combinatrics I, Wadsworth & Brooks/Cole Advanced Books, Monterey, CA, 1986.
doi: 10.1007/978-1-4615-9763-6. |
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