On the Congruences of Some Combinatorial Numbers
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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Document Type: Research Article
Affiliations: National University of Kaohsiung Chung-Kuo Institute of Technology Institute of Mathematics
Publication date: February 1, 2006