Catalan structures and Catalan pairs
نویسندگان
چکیده
منابع مشابه
Catalan structures and Catalan pairs
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced in [DFPR] with the aim of giving a common language to most of the structures counted by Catalan numbers. Here, we give a simple method to pass from the recursive definition of a generic Catalan structure to the recursive definitio...
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Dept. of Mathematics, California State University Los Angeles, Los Angeles, CA 90032, USA. Center for Combinatorics, LPMC, Nankai University, 300071 Tianjin, P.R. China. The High School Affiliated to Renmin University of China, Renmin University of China, 100080 Beijing, P.R. China. Department of Mathematics, Haifa University, 31905 Haifa, Israel. [email protected], [email protected], touf...
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Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday
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Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible generalization of the Catalan numbers. We will present a new combinatorial object that is enumerated by the k-Catalan numbers, staircase tilings. We give a bijection between staircase tilings and k-good paths, and between k-good paths and k-ary trees. In addition, we enumerate k-ary paths according to D...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2013
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2012.07.007