b-mehta / b-mehta/combinatorics

k-cascade representation

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enhancement
Dominant language
Lean
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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.

Contributor guide

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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.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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