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The Number of Snakes in a Box

Year 2018, Volume: 1 Issue: 2, 145 - 156, 25.12.2018

Christian Barrientos Sarah Minion

https://doi.org/10.33401/fujma.453324

Abstract

Within the class of polyominoes we work on the enumeration of two subfamilies of the family of snake polyominoes: stairs and snakes of height 2. We consider them from a graph theoretical perspective. In the process of enumeration of these graphs, we use classical ideas, as symmetries, and a new approach that connects these snakes with the partitions of integers.

Keywords

Partition Polyomino Snake

References

  • [1] D. Battaglino, A. Frosini, V. Guerrini, Binary pictures with excluded patters, Discrete Geometry for Computer Imagery, 18th IAPR International Conference, (2014), 25–38.
  • [2] S. W. Golomb, (2nd ed.), Polyominoes: Ouzzles, Patterns, Problems, and Packings, Princeton University Press, Princeton, MA, 1996.
  • [3] A. Goupil, M.-E. Pellerin, J. de Wouters d’Oplinter, Partially directed snake polyominoes, Discrete Appl. Math., 236 (2018), 223–234.
  • [4] E. Pegg Jr., https://oeis.org/A002013, 2009.
  • [5] C. Barrientos, Graceful labelings of cyclic snakes, Ars Combin., 60 (2001), 85–96.
  • [6] C. Barrientos, S. Minion, Snakes: from graceful to harmonious, Bull. Inst. Combin. Appl., 79 (2017), 95–107.
  • [7] N. J. A. Sloane, R. K. Guy, https://oeis.org/A005418, 2012.
  • [8] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris, (1967), 349–355.
  • [9] C. Barrientos, S. Minion, On the number of a-labeled graphs, Discuss. Math. Graph Theory, 38 (2018), 177–188.
  • [10] J. A. Gallian, A dynamic survey of graph labelings, Electron. J. Combin., (2017), #DS6.
  • [11] E. Deutsch, https://oeis.org/A102547, 2010.
  • [12] N. J. A. Sloane, https://oeis.org/A226916, 2013.
  • [13] G. McGarvey,, https://oeis.org/A102543, 2005.
  • [14] N. J .A. Sloane, https://oeis.org/A078012, 2002.

Year 2018, Volume: 1 Issue: 2, 145 - 156, 25.12.2018

Christian Barrientos Sarah Minion

https://doi.org/10.33401/fujma.453324

Abstract

References

  • [1] D. Battaglino, A. Frosini, V. Guerrini, Binary pictures with excluded patters, Discrete Geometry for Computer Imagery, 18th IAPR International Conference, (2014), 25–38.
  • [2] S. W. Golomb, (2nd ed.), Polyominoes: Ouzzles, Patterns, Problems, and Packings, Princeton University Press, Princeton, MA, 1996.
  • [3] A. Goupil, M.-E. Pellerin, J. de Wouters d’Oplinter, Partially directed snake polyominoes, Discrete Appl. Math., 236 (2018), 223–234.
  • [4] E. Pegg Jr., https://oeis.org/A002013, 2009.
  • [5] C. Barrientos, Graceful labelings of cyclic snakes, Ars Combin., 60 (2001), 85–96.
  • [6] C. Barrientos, S. Minion, Snakes: from graceful to harmonious, Bull. Inst. Combin. Appl., 79 (2017), 95–107.
  • [7] N. J. A. Sloane, R. K. Guy, https://oeis.org/A005418, 2012.
  • [8] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris, (1967), 349–355.
  • [9] C. Barrientos, S. Minion, On the number of a-labeled graphs, Discuss. Math. Graph Theory, 38 (2018), 177–188.
  • [10] J. A. Gallian, A dynamic survey of graph labelings, Electron. J. Combin., (2017), #DS6.
  • [11] E. Deutsch, https://oeis.org/A102547, 2010.
  • [12] N. J. A. Sloane, https://oeis.org/A226916, 2013.
  • [13] G. McGarvey,, https://oeis.org/A102543, 2005.
  • [14] N. J .A. Sloane, https://oeis.org/A078012, 2002.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Christian Barrientos 0000-0003-2838-8687

Sarah Minion This is me 0000-0002-8523-3369

Publication Date December 25, 2018
Submission Date August 13, 2018
Acceptance Date December 9, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Barrientos, C., & Minion, S. (2018). The Number of Snakes in a Box. Fundamental Journal of Mathematics and Applications, 1(2), 145-156. https://doi.org/10.33401/fujma.453324
AMA Barrientos C, Minion S. The Number of Snakes in a Box. FUJMA. December 2018;1(2):145-156. doi:10.33401/fujma.453324
Chicago Barrientos, Christian, and Sarah Minion. “The Number of Snakes in a Box”. Fundamental Journal of Mathematics and Applications 1, no. 2 (December 2018): 145-56. https://doi.org/10.33401/fujma.453324.
EndNote Barrientos C, Minion S (December 1, 2018) The Number of Snakes in a Box. Fundamental Journal of Mathematics and Applications 1 2 145–156.
IEEE C. Barrientos and S. Minion, “The Number of Snakes in a Box”, FUJMA, vol. 1, no. 2, pp. 145–156, 2018, doi: 10.33401/fujma.453324.
ISNAD Barrientos, Christian - Minion, Sarah. “The Number of Snakes in a Box”. Fundamental Journal of Mathematics and Applications 1/2 (December 2018), 145-156. https://doi.org/10.33401/fujma.453324.
JAMA Barrientos C, Minion S. The Number of Snakes in a Box. FUJMA. 2018;1:145–156.
MLA Barrientos, Christian and Sarah Minion. “The Number of Snakes in a Box”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 145-56, doi:10.33401/fujma.453324.
Vancouver Barrientos C, Minion S. The Number of Snakes in a Box. FUJMA. 2018;1(2):145-56.
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