Horizontal runs in domino tilings

Öz

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. Extensionsare also mentioned

Anahtar Kelimeler

• Tiling, Generating function, Asymptotic, Bootstrapping, Mellin transform, Fibonacci numbers

Kaynakça

1. P. Flajolet, X. Gourdon, P. Dumas, Mellin transforms and asymptotics: Harmonic sums, Theoretical Computer Science 144, 3-58, 1995.
2. P. Flajolet, R. Sedgewick, Analytic combinatorics, Cambridge University Press, Cambridge, 2009.
3. R. Graham, D. E. Knuth, O. Pathasnik, Concrete Mathematics, second edition, Addison Wesley, Reading, 1994.
4. C. Heuberger, H. Prodinger, Carry propagation in signed digit representations, European J. Combin, 24(3), 293-320, 2003.
5. A. Knopfmacher, H. Prodinger. On Carlitz compositions, European J. Combin, 19(5), 579-589, 1998.
6. D. E. Knuth, The average time for carry propagation, Nederl. Akad. Wetensch. Indag. Math., 40(2), 238-242, 1978.
7. G. Louchard, H. Prodinger, Asymptotics of the moments of extreme-value related distribution func- tions, Algorithmica, 46, 431-467, 2006.
8. H. Prodinger, S. Wagner, Bootstrapping and double-exponential limit laws, submitted, 2012.