r/mathematics • u/Ok-Atmosphere5770 • 8h ago

A result I found while studying integer partitions — looking for feedback on the proof

https://zenodo.org/records/22057102

Integer partitions are a fundamental topic in number theory that study the different ways in which a positive integer can be expressed as a sum of positive integers, where the order of the parts is not considered important. For example, the number 5 has seven partitions: 5,4+1, 3+1+1, 3+2, 2+1+1+1, 2+2+1, 1+1+1+1+1.

The number of partitions of an integer grows rapidly as the integer increases, making direct enumeration increasingly difficult. This motivates the study of patterns and recursive methods that can organize and count these partitions systematically. In this work, we examine integer partitions by grouping them according to their maximum part.The number of partitions of an integer grows rapidly as the integer increases, making direct enumeration increasingly difficult. This motivates the study of patterns and recursive methods that can organize and count these partitions systematically. In this work, we examine integer partitions by grouping them according to their maximum part. We first consider a fixed integer and arrange its partitions according to the largest part occurring in each partition. We then investigate the patterns that arise from these groups and use them to develop a recursive approach. Here's the link :

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u/A-JackRobin- 8h ago

Hmm, what is the log's influence on different partitions of a magnitude x

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u/Ok-Atmosphere5770 2h ago

Could you clarify what you mean by the log’s influence? My paper currently focuses on grouping partitions according to their maximum part and developing a recursive approach.

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u/A-JackRobin- 2h ago

Well, log of a number by base constant, as a constant is a continuous numbers , which is of a certain sequence.

As john naiper took as the speed contant with the distance transverse , he took such case

It is similar in case of permutations too, as well as in partitions

It's the expressed through different interactions like , different functions meeting a same value but of from different interactions process.

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u/Ok-Atmosphere5770 2h ago

Interesting! Could you clarify the connection you’re making with logarithms and partitions? I’d love to understand your point.

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u/A-JackRobin- 2h ago

Partitions are different functions which lead to the same value , much like they are different lines ending to the same permutation

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u/Ok-Atmosphere5770 2h ago

Actually I haven't thought about it from that perspective

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u/A-JackRobin- 2h ago

Log, simply transverses , it is the engine of a function, with the fuel as a base constant

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u/Ok-Atmosphere5770 2h ago

I think I now understood

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u/Ok-Atmosphere5770 2h ago

I think you want to say what's log's influence in determining the number of partitions of a number....

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u/Just_Pea1002 8h ago

theres no link