Horizontal runs in domino tilings
DOI:
https://doi.org/10.13069/jacodesmath.09554Keywords:
Tiling, Generating function, Asymptotic, Bootstrapping, Mellin transform, Fibonacci numbersAbstract
We discuss tilings of a grid (of size $n × 2$) with dominoes of size $2 × 1$. Parameters that might be called "longest run" are investigated, in terms of generating functions and also asymptotically. Extensions are also mentioned.
Received: 18 May 2014 | Accepted: 24 June 2014
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References
P. Flajolet, X. Gourdon, and P. Dumas, Mellin transforms and asymptotics: Harmonic sums, Theoret. Comput. Sci. 144(1-2) (1995) 3–58.
P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, Cambridge (2009).
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics. a Foundation for Computer Science, 2nd Edition, Addison-Wesley Professional, Reading (1994).
C. Heuberger and H. Prodinger, Carry propagation in signed digit representations, European J. Combin. 24(3) (2003) 293–320.
A. Knopfmacher and H. Prodinger, On carlitz compositions, European J. Combin. 19(5) (1998) 579–589.
D. E. Knuth, The average time for carry propagation, Indag. Math. Proc. 81(1) (1978) 238–242.
G. Louchard and H. Prodinger, Asymptotics of the moments of extreme-value related distribution functions, Algorithmica 46(3-4) (2006) 431–467.
H. Prodinger and S. Wagner, Bootstrapping and double-exponential limit laws, Discrete Math. Theor. Comput. Sci. 17(1) (2015) 123--144.
