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A unique arithmetic labeling of hexagonal lattices
Author(s) -
Chang Gerard J.,
Hwang F. K.,
Wright P. E.,
Griggs J. R.
Publication year - 1995
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.3180030303
Subject(s) - modulo , combinatorics , hexagonal crystal system , mathematics , equivalence (formal languages) , set (abstract data type) , arithmetic , discrete mathematics , computer science , chemistry , crystallography , programming language
Consider an r ‐layer hexagon consisting of 3 r 2 + 3 r + 1 hexagonal cells. Can one label the cells by the set N r = {0,1,…, 3 r 2 + 3 r } such that each line of adjacent cells are labeled by numbers forming an arithmetic progression modulo (3 r 2 + 3 r + 1) (in proper ordering)? We show that for each r there exists such a labeling unique up to equivalence. We also study some other related issues. © 1995 John Wiley & Sons, Inc.