Action Graphs and Catalan Numbers

被引：0
|
作者：
Alvarez, Gerardo [1 ]
Bergner, Julia E. [1 ]
Lopez, Ruben [1 ]
机构：
[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA
来源：
JOURNAL OF INTEGER SEQUENCES | 2015年 / 18卷 / 07期
关键词：
Catalan number; directed graph;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce an indutively defined sequence of directed graphs and prove that the number of edges added at step k is equal to the kth Catalan number. Furthermore, we establish a bijection between the set of edges adjoined at step k and the set of planar rooted trees with k edges.
引用
收藏
页数：7
相关论文
共 50 条
  • [41] ANOTHER APPEARANCE OF THE CATALAN NUMBERS
    WELLS, DM
    AMERICAN MATHEMATICAL MONTHLY, 1986, 93 (03): : 217 - 218
  • [42] SOME PROPERTIES OF CATALAN NUMBERS
    SCOVILLE, R
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (07): : A602 - A602
  • [43] CATALAN NUMBERS IN PROCESS SYNTHESIS
    SHOAEI, M
    SOMMERFELD, JT
    AICHE JOURNAL, 1986, 32 (11) : 1931 - 1933
  • [44] Arithmetic of weighted Catalan numbers
    Gao, Yibo
    Gu, Andrew
    JOURNAL OF NUMBER THEORY, 2021, 226 : 213 - 242
  • [45] Q-CATALAN NUMBERS
    FURLINGER, J
    HOFBAUER, J
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 1985, 40 (02) : 248 - 264
  • [46] Catalan, Motzkin, and Riordan numbers
    Bernhart, FR
    DISCRETE MATHEMATICS, 1999, 204 (1-3) : 73 - 112
  • [47] Fedosov differentials and Catalan numbers
    Loeffler, Johannes
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (23)
  • [48] Catalan numbers with mersenne subscripts
    Koshy, Thomas
    Gao, Zhenguang
    Mathematical Scientist, 2013, 38 (02): : 86 - 91
  • [49] Alternating Convolutions of Catalan Numbers
    Wenchang Chu
    Bulletin of the Brazilian Mathematical Society, New Series, 2022, 53 : 95 - 105
  • [50] Tribinomial coefficients and Catalan numbers
    Koshy, Thomas
    Salmassi, Mohammad
    MATHEMATICAL GAZETTE, 2009, 93 (528): : 449 - 455
12345