# 学术报告（Salvatore Tringali 12.10）

## Additive decompositions of sets of integers into irreducible sets (对整数集的子集的不可约加法分解)

Additive decompositions of sets of integers into irreducible sets (对整数集的子集的不可约加法分解)

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Salvatore Tringali副教授 河北师范大学数学科学学院

X=A1+...+An :={a1+...+an : a1A1, ... , an∈An}.

It was conjectured in [1, § 5] that, for every non-empty finite subset L of Z2, there exists a subset X of Z such that L(X) = L. I will survey what (little) is known about this conjecture and frame the problem within the broader context of factorization theory.

Reference:

[1] Y. Fan, S. Tringali, Power monoids: A bridge between factorization theory and arithmetic combinatorics, J. Algebra 512 (2018) 252-294.

Z是整数环。Z的一个子集A称为不可约的，若A的元素个数不为1，且A不能写成两个Z中集合XY之和，其中X和Y都不是独元集。因此，对一个至少有两个元素的Z的子集X，记L(X)为所有满足下面条件的正整数之集：X可以表为n个不可约集之和。