We prove that any large even Artin group is poly-free and based on a triangle graph also poly-free.

A computational group is pseudo-free if an adversary cannot find solutions in this group for equations that are not trivially solvable in the free group. This notion was put forth by Rivest as a unifying abstraction of multiple group-related hardness assumptions commonly used in cryptography. Rivest’s conjecture that the RSA group is pseudo-free had been settled by Micciancio for the case of RS...

Our main goal is to study the freeness of Schützenberger groups defined by primitive substitutions. findings include a simple test for these groups, which applied exhibit invertible substitution with corresponding non-free group. This constitutes counterexample result Almeida dating back 2005. We also give some early results concerning relative question remains largely unexplored.

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...

We study the problem of fair division when resources contain both divisible and indivisible goods. Classic fairness notions such as envy-freeness (EF) up to one good (EF1) cannot be directly applied mixed goods setting. In this work, we propose a new notion for (EFM), which is direct generalization EF EF1 prove that an EFM allocation always exists any number agents. also efficient algorithms co...

In the theory of operator algebras, classification of group actions on approximately finite dimensional (AFD) factors has been done since Connes’s work [2]. In subfactor theory, various results on classification of group actions have been obtained. The most powerful results have been obtained by Popa in [16], who classified the strongly outer actions of discrete amenable groups on strongly amen...