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- W1977488599 abstract "A word u is called 1-balanced if for any two factors v and w of u of equal length, we have −1⩽|v| i −|w| i ⩽1 for each letter i , where |v| i denotes the number of occurrences of i in the factor v . The aim of this paper is to extend the notion of balance to multi-dimensional words. We first characterize all 1-balanced words on Z n . In particular, we prove they are fully periodic for n>1 . We then give a quantitative measure of non-balancedness for some words on Z 2 with irrational density, including two-dimensional Sturmian words." @default.
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- W1977488599 date "2002-02-01" @default.
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- W1977488599 title "Balance properties of multi-dimensional words" @default.
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- W1977488599 doi "https://doi.org/10.1016/s0304-3975(00)00441-2" @default.
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