Published 2021-01-01
“…A set of positive integers <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> is called a Golomb ruler if the difference between two distinct elements of <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> are different, equivalently if the sums of two elements are different (<inline-formula> <tex-math notation="LaTeX">$B_{2}$ </tex-math></inline-formula> set,
Sidon set). An extension of this concept is to consider that the sum of <inline-formula> <tex-math notation="LaTeX">$h $ </tex-math></inline-formula> elements in <inline-formula> <tex-math notation="LaTeX">$A $ </tex-math></inline-formula> are all different, except for permutation of the summands, with <inline-formula> <tex-math notation="LaTeX">$h \geq 2 $ </tex-math></inline-formula>, in this case it is said that <inline-formula> <tex-math notation="LaTeX">$A $ </tex-math></inline-formula> is a set <inline-formula> <tex-math notation="LaTeX">$B_{h} $ </tex-math></inline-formula>, the length of <inline-formula> <tex-math notation="LaTeX">$A $ </tex-math></inline-formula> is given by <inline-formula> <tex-math notation="LaTeX">$\ell (A)\,\,= \max A- \min A $ </tex-math></inline-formula>. …”
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