1. **EENN** 2. **ENEN** 因此,从 (0, 0) 到 (2, 2) 的合法Dyck路径总共有 2 条。 三、命题:在n×n网格中,越过交叉y=x线的格子路径与(n-1)×(n+1)网格中的格子路径之间存在一一对应的双射关系。 四、卡特兰数Catalan Numbers的推导 想象一个游戏 首先,想象一下我们在玩一个“路径游戏”。...
Where does n+1 come from in the formula for Catalan numbers? Why is it not n? Consider sequences of X's and Y's, where we can form a Dyck word only if every prefix has at least as many X's as Y's Now consider this argument: for any sequence consisting equally of X's and ...
QI N D K,XIE H M.Catalan numbers,dycklanguage and ti me series of elementary cellular automaton of rule56. Journal of Systems Science and Complexity . 2005QIN D K,XIE H M. Catalan numbers,dyck language and time series of elementary cellular automaton of rule 56[J].Journal of Systems ...
This recovers the result shown in [33], namely that Dyck paths without UDUs are enumerated by the Motzkin numbers. Enumeration of k-ary paths according to the number of UU. Note that adjacent rows with the same size border tile in a BHR-tiling create an occurrence of UU in the k-ary ...
Dyck路的个数。 Riordan群R中形如(1,h(t))的 Riordan矩阵构成的子群,称为 Lagrange子群。我们在 Lagrange子群对上述三类 Catalan矩阵进行推广,引入了相应的广义 Catalan矩阵的概念,并给出其组合解释。 第一类 Catalan矩阵(C(t),tC(t))的A序列发生函数为 ,在 Lagrange子群中,其A序列为A 1=(c,cr,cr 2,…...
This is proved by exhibiting weight-preserving bijections between the given collections and the set of Dyck paths. The bijections are based on encodings of Dyck paths and permutations as sequences of partitions. 展开 DOI: 10.1016/j.ejc.2004.01.006 被引量: 8 ...
A Distributive Lattice Structure Connecting Dyck Paths, Noncrossing Partitions and 312-avoiding Permutations In [Ferrari, L. and Pinzani, R.: Lattices of lattice paths. J. Stat. Plan. Inference 135 (2005), 77–92] a natural order on Dyck paths of any fixed length... E Barcucci,A Bernin...
A class of well-formed sets of associated opening and closing parentheses is well studied in conjunction with Dyck paths and Catalan numbers. Nested parenthes... RJ Mathar 被引量: 1发表: 2016年 The Relationship of Multiset, Stirling Number, Bell Number, and Catalan Number Catalan numbers was ...
被引量: 171发表: 1999年 Counting peaks at height in a Dyck path. 02.1.1, 10 p., electronic onlyLA - engKW - Dyck paths; Catalan numbers; Chebyshev polynomialsUR - http://eudml.org/doc/49999ER -Mansour, Toufik... T Mansour 被引量: 62发表: 2002年 ...
In passing, we also show a correspondence with Dyck paths, the Catalan and Fine numbers. We present an algorithm for winning the Normal Play game on ... Richard,J.,Nowakowski,... - 《Journal of Combinatorial Mathematics & Combinatorial Computing》 被引量: 3发表: 2013年 The Art of Romare...