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Group actions and hashing unordered multisets (2021)
I learned of a neat result due to Kevin Ventullo that uses group actions to study the structure of hash functions for unordered sets and multisets. This piqued my interest because a while back a colleague asked me if I could think of any applications of “pure” group theory to practical computer programming that were not cryptographic in nature. He meant, not including rings, fields, or vector spaces whose definitions happen to be groups when you forget the extra structure.
I learned of a neat result due to Kevin Ventullo that uses group actions to study the structure of hash functions for unordered sets and multisets. This piqued my interest because a while back a colleague asked me if I could think of any applications of “pure” group theory to practical computer programming that were not cryptographic in nature. To give more detail, we need to review some group theory, write down the formal properties of an accumulative hash function, and prove the structure theorem.
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