2 papers
math.CO2025
Average-Rare Order Ideals in Functional Preorders
Masahiro Hachimori, Kenji Kashiwabara
We prove that for the preorder induced by a function f: V -> V, the family of all order ideals is average-rare, that is, its normalized degree sum (nds) is nonpositive. As a base c…
math.CO2025
On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4
Masahiro Hachimori, Kenji Kashiwabara
Frankl's conjecture, also known as the union-closed sets conjecture, can be equivalently expressed in terms of intersection-closed set families by considering the complements of se…