Abstract
Björner and Welker studied homology of k-equal partition lattices and obtained interesting identities for (n - 1)!. In this article, simple combinatorial proofs of these identities are discussed.
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Suggested Reading
A Björner and V Welker, The homology of “k-equal” manifolds and related partition lattices, Advances in Math., Vol.110, pp.277–313, 1995.
A Björner and M Wachs, Shellable nonpure complexes and posets, I, Trans. Amer. Math. Soc, Vol.348, pp.1299–1327, 1996.
R P Stanley, Enumerative Combinatorics Vol.1, Cambridge Studies in Advanced Mathematics, Vol.49, Cambridge Univ. Press, Cambridge, 1997.
G E Bredon, Topology and Geometry, Graduate text in mathematics Vol.139, Springer-Verlag, New York, 1993.
A Hatcher, Algebraic Topology, Cambridge Univ. Press, Cambridge, 2002.
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Thanks are due to the anonymous referee and the editorial team for many valuable suggestions.
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Kumar, C. Two Identities. Reson 24, 1151–1165 (2019). https://doi.org/10.1007/s12045-019-0882-5
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DOI: https://doi.org/10.1007/s12045-019-0882-5