Year: 2025
Type: article
Abstract: An amoeba is a tree together with instructions how to iteratively grow trees by adding paths of a fixed length $$\ell $$ ℓ . This paper analyses such a growth process. An amoeba is mortal if all versions of the process are finite, and it is immortal if they are all infinite. We obtain some necessary and some sufficient conditions for mortality. In particular, for growing caterpillars in the case $$\ell =1$$ ℓ = 1 we characterize mortal amoebas. We discuss variations of the mortality concept, conjecture that some of them are equivalent, and support this conjecture for $$\ell \in \{1,2\}$$ ℓ ∈ { 1 , 2 } .
Source: Results in Mathematics
Authors: Vladimir Gurvich, Matjaž Krnc, Mikhail Vyalyi
Institutions: Rutgers, The State University of New Jersey, National Research University Higher School of Economics, University of Primorska, Russian Academy of Sciences, Moscow Institute of Physics and Technology, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4410659068