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Recent advances in graph theory, linear algebra, and commutative algebra render us to tackle problems in one bough of mathematics with assistance and guidance from others. We will elaborate foremost and conceptually fathomless homological invariants inextricably linked with circulant matrices and cycles through various path lengths in this article, as well as a class of Koszul algebra, which portrays combinatorial correlation, in the end.

A Class of Koszul Algebra and Some Homological Invariants through Circulant Matrices and Cycles