An identity for vertically aligned entries in Pascal’s triangle

Heidi Goodson
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 2, Pages 213—221
DOI: 10.7546/nntdm.2020.26.2.213-221
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Authors and affiliations

Heidi Goodson
Department of Mathematics, Brooklyn College
2900 Bedford Avenue, Brooklyn, NY 11210 USA

Abstract

The classic way to write down Pascal’s triangle leads to entries in alternating rows being vertically aligned. In this paper, we prove a linear relation on vertically aligned entries in Pascal’s triangle. Furthermore, we give an application of this relation to morphisms between hyperelliptic curves.

Keywords

  • Pascal’s triangle
  • Binomial coefficients
  • Hyperelliptic curves

2010 Mathematics Subject Classification

  • 05A10
  • 11G30

References

  1. Emory, M., Goodson, H., & Peyrot, A. (2018). Towards the Sato–Tate Groups of Trinomial Hyperelliptic Curves. ArXiv e-prints, page arXiv:1812.00242, Dec. 2018.
  2. Koshy, T. (2014). Pell and Pell–Lucas numbers with applications. Springer, New York.
  3. Miranda, R. (1995). Algebraic curves and Riemann surfaces, Volume 5 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI.
  4. Silverman, J. H. (2009). The arithmetic of elliptic curves, Volume 106 of Graduate Texts in Mathematics. Springer, Dordrecht, Second edition.
  5. Sloane, N. J. A. (2018). Sequence A034807. The On-Line Encyclopedia of Integer Sequences. Available online at: https://oeis.org/A034807.
  6. Stanley, R.P.(1999). Enumerative Combinatorics. Volume 2, Cambridge Studies in Advanced Mathematics, Volume 62. Cambridge University Press, Cambridge.
  7. Stanley, R.P.(2012). Enumerative Combinatorics. Volume 1, Cambridge Studies in Advanced Mathematics, Volume 49. Cambridge University Press, Cambridge, Second edition.

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Cite this paper

Goodson, H. (2020). An identity for vertically aligned entries in Pascal’s triangle. Notes on Number Theory and Discrete Mathematics, 26 (2), 213-221, doi: 10.7546/nntdm.2020.26.2.213-221.

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