TY - JOUR

T1 - Prime Factorization of Meanders

AU - Белоусов, Юрий Станиславович

PY - 2026/5/8

Y1 - 2026/5/8

N2 - This paper introduces a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated snakes and irreducible meanders. We find out that iterated snakes allow efficient enumeration, and thus the problem of enumerating meanders reduces to the problem of enumerating irreducible meanders. Additionally, we present some results concerning the asymptotics of meanders of both classes.

AB - This paper introduces a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated snakes and irreducible meanders. We find out that iterated snakes allow efficient enumeration, and thus the problem of enumerating meanders reduces to the problem of enumerating irreducible meanders. Additionally, we present some results concerning the asymptotics of meanders of both classes.

UR - https://www.mendeley.com/catalogue/af812220-bfc9-33cb-b810-f84de1121d3f/

U2 - 10.37236/13636

DO - 10.37236/13636

M3 - Article

VL - 33

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1097-1440

IS - 2

M1 - P2.28

ER -