Work

Single Polygon Counting for $m$ Fixed Nodes in Cayley Tree: Two Extremal Cases

Year: 2010

Type: preprint

Abstract: We denote a polygon as a connected component in Cayley tree of order 2 containing certain number of fix vertices. We found an exact formula for a polygon counting problem for two cases, in which, for the first case the polygon contain a full connected component of a Cayley tree and for the second case the polygon contain two fixed vertices. From these formulas, which is in the form of finite linear combination of Catalan numbers, one can find the asymptotic estimation for a counting problem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1004.2305

Authors: Mukhamedov, Farrukh, Pah, Chin Hee, Saburov, Mansoor

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1672956166

Cites: 12

Cited by: 1

Related to: 10