Premium
On the Congruences of Some Combinatorial Numbers
Author(s) -
Eu SenPeng,
Liu ShuChung,
Yeh YeongNan
Publication year - 2006
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2006.00337.x
Subject(s) - congruence relation , mathematics , combinatorics , conjecture , class (philosophy) , catalan number , discrete mathematics , computer science , artificial intelligence
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.