I understand from the fundamental theorem of arithmetic that every number can be written as a product of its prime factors,but I’m curious about partitions,how numbers can be broken up into sums and differences.What books would be necessary for me to develop a good theoretical intuition concerning partitions?Is there also a subfield field of number theory dedicated to the study of partitions?
$\begingroup$
$\endgroup$
3
-
$\begingroup$ It's hard to know what you mean without more details than this. What are you interested in about partitions? Counting them? What kind? Does order matter or not (this dramatically affects the answer)? $\endgroup$– Qiaochu YuanCommented Jan 24, 2023 at 23:15
-
$\begingroup$ Partitions are considered part of number theory and also combinatorics. A good place to start is the Wikipedia artice Partition (number theory). Of the books listed as references in Wikipedia, perhaps the most elementary is A Walk Through Combinatorics by Bona. $\endgroup$– awkwardCommented Jan 25, 2023 at 15:09
-
$\begingroup$ I highly recommend George Andrews & Kimmo Eriksson's Integer Partitions (Cambridge, 2004) for an approachable yet substantive treatment. $\endgroup$– Brian HopkinsCommented Jan 28, 2023 at 19:43
Add a comment
|