On the Congruences of Some Combinatorial Numbers

  1. Sen-Peng Eu,
  2. Shu-Chung Liu,
  3. Yeong-Nan Yeh

Article first published online: 20 DEC 2005

DOI: 10.1111/j.1467-9590.2006.00337.x

Issue

Studies in Applied Mathematics

Studies in Applied Mathematics

Volume 116, Issue 2, pages 135–144, February 2006

Additional Information

How to Cite

Eu, S.-P., Liu, S.-C. and Yeh, Y.-N. (2006), On the Congruences of Some Combinatorial Numbers. Studies in Applied Mathematics, 116: 135–144. doi: 10.1111/j.1467-9590.2006.00337.x

Author Information

  1. National University of Kaohsiung Chung-Kuo Institute of Technology Institute of Mathematics

*Address for correspondence: Shu-Chung Liu, Institute of Mathematics, Academia Sinica, Nankang, Taipei, 11529, Taiwan; e-mail: liularry@ms.ckitc.edu.tw

Publication History

  1. Issue published online: 20 DEC 2005
  2. Article first published online: 20 DEC 2005
  3. (Received December 3, 2004)

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In this paper, we apply Lucas' theorem to evaluate the congruences of several combinatorial numbers, including the central Delannoy numbers and a class of Apéry-like numbers, the numbers of noncrossing connected graphs, the numbers of total edges of all noncrossing connected graphs on n vertices, etc. One of these results verifies a conjecture given by Deutsch and Sagan recently. In the end, we use an automaton to explain the idea of our approach.

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