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Eretrandre Mathematics Reference Database -- Query Results
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Author Trappmann, H.; Ziegler, G.M.
Title Shellability of complexes of trees Type Journal Article
Year 1998 Publication J. Comb. Theory, Ser. A Abbreviated Journal
Volume 82 Issue 2 Pages 168-178
Keywords shellability; simplicial complex; Cohen-Macaulay complex; free Lie algebra; tree complex
Abstract Let ${\cal F}^{(k)}{n}$ be a simplicial complex of dimension $n-2$ whose facets correspond to the leaf-labelled trees with $n$ interior vertices of degree exactly $k+1$. This complex has interesting applications in homotopy theory, in the representation theory of symmetric groups and in the theory of free Lie $k$-algebras. Previously it has been proved by {\it P. Hanlon} [J. Comb. Theory, Ser. A 74, 301-320 (1996; Zbl 0848.05021)] that ${\cal F}^{(k)}{n}$ are Cohen-Macaulay. The paper under review provides a proof of shellability of ${\cal F}^{(k)}_{n}$. Additionally an explicit basis for the homology of this complex is obtained; this basis is equivalent to the basis constructed by {\it P. Hanlon} and {\it M. Wachs} [Adv. Math. 113, 206-236 (1995; Zbl 0844.17001)] for the multiplicity-free part of the free Lie $k$-algebra. The main result of this paper was also obtained independently by M. Wachs.
Corporate Author Thesis
Publisher Place of Publication Editor (up)
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
Area Expedition Conference
Notes Approved no
Call Number EE @ henryk @ ref0916.06004
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