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Shellable nonpure complexes and posets. II. (English) Zbl 0886.05126
This paper represents the promised continuation of a first important paper introducing a theory of shellability of simplicial complexes and posets in full generality and with it the completion of the subject as described in that first paper, see A. Björner and M. L. Wachs [ibid. 348, No. 4, 1299-1327 (1996; Zbl 0857.05102)]. The major effort here is to present further important classes of possibly nonpure posets and their complexes and to treat them along the lines developed in the general theory of part I which is continued in this part II through investigations into what variety of constructions preserve shellability to which some answers are provided and then to apply these concepts to algebraic aspects of the theory also. Thus the Stanley-Reisner rings consider in some detail these situations as well. Taken all together, these two publications may form a good basis for a course or seminar at a suitably advanced level for students or faculty with a serious interest in the subject.

MSC:
05E99 Algebraic combinatorics
06A11 Algebraic aspects of posets
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
55U15 Chain complexes in algebraic topology
57Q05 General topology of complexes
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