A bijection is introduced in the set of all Dyck paths of semilength n from which it follows that (i) the parameters 'height of the first peak' and 'number of returns' have the same distribution and (ii) the parameter 'number of high peaks' has the Narayana distribution.
A Bijection on Ordered Trees and Its Consequences
โ Scribed by Emeric Deutsch
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 214 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
โฆ Synopsis
A bijection is introduced in the set of all ordered trees having n edges from which one derives that, for each positive integer q, the parameters "number of nodes of degree q" and "number of odd-level nodes of degree q-1" are equidistributed.
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In accordance with the principle from other branches of mathematics that it is better to exhibit an explicit isomorphism between two objects than merely to prove that they are isomorphic, we adopt the general principle that it is better to exhibit one-to-one correspondence (bijection) between two se
A bijection is given between the set of directed column-convex polyominoes of area n and the set of ordered trees of height at most three and having n edges. Additional bijections with less well known combinatorial objects are sketched.