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Horizontal runs in domino tilings

Year 2014, Volume: 1 Issue: 1, 19 - 27, 01.03.2014

Kamilla Oliver Helmut Prodinger

https://doi.org/10.13069/jacodesmath.09554

Abstract

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

Keywords

Tiling Generating function Asymptotic Bootstrapping Mellin transform Fibonacci numbers

References

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

Year 2014, Volume: 1 Issue: 1, 19 - 27, 01.03.2014

Kamilla Oliver Helmut Prodinger

https://doi.org/10.13069/jacodesmath.09554

Abstract

References

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

Details

Primary Language English
Journal Section Articles
Authors

Kamilla Oliver This is me

Helmut Prodinger

Publication Date March 1, 2014
Published in Issue Year 2014 Volume: 1 Issue: 1

Cite

APA Oliver, K., & Prodinger, H. (2014). Horizontal runs in domino tilings. Journal of Algebra Combinatorics Discrete Structures and Applications, 1(1), 19-27. https://doi.org/10.13069/jacodesmath.09554
AMA Oliver K, Prodinger H. Horizontal runs in domino tilings. Journal of Algebra Combinatorics Discrete Structures and Applications. March 2014;1(1):19-27. doi:10.13069/jacodesmath.09554
Chicago Oliver, Kamilla, and Helmut Prodinger. “Horizontal Runs in Domino Tilings”. Journal of Algebra Combinatorics Discrete Structures and Applications 1, no. 1 (March 2014): 19-27. https://doi.org/10.13069/jacodesmath.09554.
EndNote Oliver K, Prodinger H (March 1, 2014) Horizontal runs in domino tilings. Journal of Algebra Combinatorics Discrete Structures and Applications 1 1 19–27.
IEEE K. Oliver and H. Prodinger, “Horizontal runs in domino tilings”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 1, no. 1, pp. 19–27, 2014, doi: 10.13069/jacodesmath.09554.
ISNAD Oliver, Kamilla - Prodinger, Helmut. “Horizontal Runs in Domino Tilings”. Journal of Algebra Combinatorics Discrete Structures and Applications 1/1 (March 2014), 19-27. https://doi.org/10.13069/jacodesmath.09554.
JAMA Oliver K, Prodinger H. Horizontal runs in domino tilings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1:19–27.
MLA Oliver, Kamilla and Helmut Prodinger. “Horizontal Runs in Domino Tilings”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 1, no. 1, 2014, pp. 19-27, doi:10.13069/jacodesmath.09554.
Vancouver Oliver K, Prodinger H. Horizontal runs in domino tilings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1(1):19-27.