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Harmonic Distributions for Equitable Partitions of a Hypercube
Author(s) -
Hyun Jong Yoon
Publication year - 2015
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21412
Subject(s) - mathematics , hypercube , partition (number theory) , adjacency matrix , eigenfunction , harmonic , combinatorics , orthogonal array , adjacency list , characterization (materials science) , discrete mathematics , eigenvalues and eigenvectors , graph , statistics , physics , quantum mechanics , taguchi methods , optics
We provide general criteria for orthogonal arrays and t‐designs on equitable partitions of a hypercube Q n by exploring harmonic distributions. Generalized harmonic weight enumerators for real‐valued functions of Q n are introduced and applied to eigenfunctions of the adjacency matrix of Q n . Using this, expressions for harmonic distributions are established for every cell of an equitable partition π of Q n . Moreover, for any given cell in the partition π, the strength of the cell as an orthogonal array is explicitly expressed, and also a characterization of a t‐design of that cell is established. We also compute strengths of cells and find t‐designs from cells based on constructions of Krotov, Borges, Rifa, and Zinoviev.