Percolating sets and the operad of permutations
Denis Bashkirov
TL;DR
This paper provides an operadic framework to understand percolating permutation matrices and explores the algebraic structures related to percolation properties in permutation operads.
Contribution
It introduces an operadic interpretation of percolating permutation matrices and relates ideals and suboperads to percolation properties in a novel algebraic context.
Findings
Operadic interpretation of percolating permutation matrices
Relation between ideals/suboperads and percolation properties
Presentation of the permutation operad
Abstract
We give an operadic interpretation of the known result of L.Shapiro and A.B.Stephens that characterizes percolating permutation matrices. A relation of ideals and suboperads of the non-symmetric operad of permutations to percolative properties of sets in the 2-neighbor percolation process is discussed. On a related note, we discuss a certain presentation of the operad of permutations.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · Advanced Mathematical Identities