A Künneth Formula for Finite Sets

Chong Wang; Shiquan Ren; Jian Liu

doi:10.1007/s11401-021-0292-3

Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (6) : 801 -812. DOI: 10.1007/s11401-021-0292-3

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A Künneth Formula for Finite Sets

Chong Wang ¹^,⁴
, Shiquan Ren ²
, Jian Liu ³^,^c

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Abstract

In this paper, the authors define the homology of sets, which comes from and contains the ideas of path homology and embedded homology. Moreover, A Künneth formula for sets associated to the homology of sets is given.

Keywords

Künneth formula / Finite set / Principal ideal domain / Cartesian product / Free R-module

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Chong Wang, Shiquan Ren, Jian Liu. A Künneth Formula for Finite Sets. Chinese Annals of Mathematics, Series B, 2021, 42(6): 801-812 DOI:10.1007/s11401-021-0292-3

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References

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[1]	Berge C. Graphs and Hypergraphs, 1973, Amsterdam: North-Holland Mathematical Library

[2]	Bressan S, Li J, Ren S, Wu J. The embedded homology of hypergraphs and applications. Asian J. Math., 2019, 23(3): 479-500

[3]	Emtander E. Betti numbers of hypergraphs. Commun. Algebra, 2009, 37(5): 1545-1571

[4]	Grigor’yan, A., Lin, Y., Muranov, Y. and Yau, S. T., Homologies of path complexes and digraphs, arX-iv:1207.2834, 2012.

[5]	Grigor’yan A, Muranov Y, Vershinin V, Yau S T. Path homology theory of multigraphs and quivers. Forum Math., 2018, 30(5): 1319-1337

[6]	Grigor’yan A, Muranov Y, Yau S T. Homologies of digraphs and Künneth formulas. Commun. Anal. Geom., 2017, 25(5): 969-1018

[7]	Hatcher A. Algebraic Topology, 2001, Cambridge: Cambridge University Press

[8]	Newman M. Integral Matrices, pure Applied Mathematics, Vol. 45, 1972, New York and London: Academic Press

[9]	Parks, A. D. and Lipscomb, S. L., Homology and hypergraph acyclicity: A combinatorial invariant for hypergraphs, Naval Surface Warfare Center, 1991.