We define a tracial analog of the notion called sequentially split $$^*$$ -homomorphism between $$C^*$$ -algebras due to Barlak and Szabó show that several important approximation properties related classification theory pass from target algebra domain algebra. Then, we this framework arises Rokhlin finite group action an inclusion unital -algebras.

We study the following variant of 15 puzzle. Given a graph and two token placements on vertices, we want to find walk minimum length (if any exists) such that sequence swappings along obtains one given from other one. This problem was introduced as Sequential Token Swapping by Yamanaka et al. [JGAA 2019], who showed is intractable in general but polynomial-time solvable for trees, complete grap...

We consider a class of hypergraphs called hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is shellable or sequentially the Cohen--Macaulay if and only if $nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.