@MISC{Kemnitz_whatis, author = {A. Kemnitz and V. Soltan}, title = {What is the Minimum Length of a Non-Extendable Lace?}, year = {} }

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Abstract

A family fC 1 ; : : : ; C n g of pairwise distinct, non-overlapping, congruent circles in the plane form a lace provided C i touches C i+1 for all i = 1; : : : ; n \Gamma 1. If, additionally, C n touches C 1 , the lace is named a loop. A lace (loop) fC 1 ; : : : ; C n g is called extendable if it is properly contained in another lace (respectively, loop). In the paper various problems and results on minimum lengths of non-extendable laces and loops are discussed. Key words. Finite packing, circles, plane. AMS subject classification. 52C15 1 Main Problems and Results According to [1], a family of n non-overlapping congruent circles C 1 ; : : : ; C n form a snake of length n provided C i touches C j if and only if ji \Gamma jj = 1. We will say that a snake fC 1 ; : : : ; C n g is extendable provided it is a proper subset of another snake. (Note that in [1] and [2] non-extendable snakes are called limited and maximal, respectively.) It is proved in [1] that the minimum length of a ...