{"id":341726,"date":"2016-12-27T10:15:55","date_gmt":"2016-12-27T18:15:55","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=341726"},"modified":"2018-10-16T21:25:27","modified_gmt":"2018-10-17T04:25:27","slug":"partition-identities-coin-exchange-problem","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/partition-identities-coin-exchange-problem\/","title":{"rendered":"Partition Identities and the Coin Exchange Problem"},"content":{"rendered":"<p>The number of partitions of n into parts divisible by <em>a<\/em> or <em>b<\/em> equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of <em>a<\/em> and <em>b<\/em>. This generalizes identities of MacMahon and Andrews. The analogous identities for three or more integers (in place of <em>a<\/em>, <em>b<\/em>) hold in certain cases.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The number of partitions of n into parts divisible by a or b equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of a and b. This generalizes identities of MacMahon and Andrews. 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