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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…
math.CO2021
The root distributions of Ehrhart polynomials of free sums of reflexive polytopes
Masahiro Hachimori, Akihiro Higashitani, Yumi Yamada
In this paper, we study the root distributions of Ehrhart polynomials of free sums of certain reflexive polytopes. We investigate cases where the roots of the Ehrhart polynomials o…