Maximal evenness: Difference between revisions
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Case 1: ME(''n'', ''m'') where {{nowrap|''n'' < {{frac|''m''|2}}}}. This is a maximally even subset of Z/mZ with step sizes {{nowrap|L > s > 1}}, which determines the locations of step sizes of 2 in the complement. The rest of the complement's step sizes are 1. The sizes of the chunks of 1 are {{nowrap|L − 2}} and {{nowrap|s − 2}} (0 is a valid chunk size), and the sizes form a maximally even MOS. | Case 1: ME(''n'', ''m'') where {{nowrap|''n'' < {{frac|''m''|2}}}}. This is a maximally even subset of Z/mZ with step sizes {{nowrap|L > s > 1}}, which determines the locations of step sizes of 2 in the complement. The rest of the complement's step sizes are 1. The sizes of the chunks of 1 are {{nowrap|L − 2}} and {{nowrap|s − 2}} (0 is a valid chunk size), and the sizes form a maximally even MOS. | ||
Case 2: ME(''n'', ''m'') where {{nowrap|''n'' > {{frac|''m''|2}}}}. This has step sizes 1 and 2. The chunks of 1 (of nonzero size since {{nowrap|''n'' > {{frac|''m''|2}}}} occupy a maximally even subset of the slots of ME(''n'', ''m'') (*). Now replace each 1 with "|" and each 2 with "$|". | Case 2: ME(''n'', ''m'') where {{nowrap|''n'' > {{frac|''m''|2}}}}. This has step sizes 1 and 2. The chunks of 1 (of nonzero size since {{nowrap|''n'' > {{frac|''m''|2}}}}) occupy a maximally even subset of the slots of ME(''n'', ''m'') (*). Now replace each 1 with "|" and each 2 with "$|". | ||
(e.g.) {{nowrap|2112111 → <nowiki>$|||$||||</nowiki>}} | (e.g.) {{nowrap|2112111 → <nowiki>$|||$||||</nowiki>}} | ||