b-mehta / b-mehta/combinatorics
k-cascade representation
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Description
[An alternate way of stating KK](https://en.wikipedia.org/wiki/Kruskal%E2%80%93Katona_theorem#Statement_for_uniform_hypergraphs) uses the k-cascade representation of an integer. It would be nice to formalise this ([see Def 3 here](http://discretemath.imp.fu-berlin.de/DMII-2015-16/kruskal.pdf)) with existence and uniqueness, and state (iterated) KK in this form, so we have an explicit expression for the minimum shadow size.
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Research direction
Start by reading Definition 3 in the linked Kruskal–Katona notes and compare it with the alternate statement linked in the issue. Then inspect the repository’s existing formalizations to determine where the k-cascade representation belongs. Done means formalizing existence and uniqueness and stating iterated Kruskal–Katona in this form, with an explicit minimum-shadow expression.
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Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 35/100