ar X iv : 0 90 9 . 19 31 v 1 [ m at h . C O ] 1 0 Se p 20 09 BUCHSBAUM * COMPLEXES
نویسنده
چکیده
We introduce a class of simplicial complexes which we call Buchsbaum* over a field. Buchsbaum* complexes generalize triangulations of orientable homology manifolds. By definition, the Buchsbaum* property depends only on the geometric realization and the field. Characterizations in terms of simplicial and local cohomology are given. It is shown that Buchsbaum* complexes are doubly Buchsbaum. Applications to enumerative and graph theoretic properties of Buchsbaum* complexes are provided. The former lead to a conjecture which extends a version of the g-conjecture by Björner and Swartz. It is shown that various constructions, among them one which generalizes convex ear decompositions, yield Buchsbaum* simplicial complexes.
منابع مشابه
ar X iv : 0 90 8 . 31 74 v 2 [ m at h . C O ] 1 2 Se p 20 09 MÖBIUS TRANSFORM , MOMENT - ANGLE COMPLEXES AND HALPERIN – CARLSSON CONJECTURE
In this paper, we give an algebra–combinatorics formula of the Möbius transform for an abstract simplicial complex K on [m] = {1, ...,m} in terms of the Betti numbers of the Stanley–Reisner face ring of K. Furthermore, we employ a way of compressing K to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex...
متن کاملar X iv : 0 90 9 . 31 70 v 1 [ m at h . R A ] 1 7 Se p 20 09 On the explicit Lipshitz constant for the joint spectral radius ∗
In 2002 F. Wirth has proved that the joint spectral radius of irreducible compact families of matrices is locally Lipshitz continuous as a function of the matrix family. In the paper, an explicit formula for the related Lipshitz constant is obtained. PACS number 02.10.Ud; 02.10.Yn MSC 2000: 15A18; 15A60
متن کاملar X iv : 0 90 9 . 29 83 v 1 [ m at h . N T ] 1 6 Se p 20 09 COMBINATORIAL IDENTITIES INVOLVING THE MÖBIUS FUNCTION
In this paper we derive some identities and inequalities on the Möbius mu function. Our main tool is phi functions for intervals of positive integers and their unions.
متن کاملar X iv : h ep - p h / 03 09 33 9 v 1 3 0 Se p 20 03 SIT - HEP / TM - 19 Q ball inflation
We show that inflation can occur in the core of a Q-ball.
متن کاملEnumerating labeled graphs with a k-cycle
Cayley’s Tree Formula for enumerating labeled trees is well known. In this paper a more general result is presented for graphs with exactly one k-cycle (i.e. cycle on k vertices ).It is proved that for all integers n and k such that (n ≥ k ≥ 3), the number of possible labeled graphs on n vertices that contain exactly one k-cycle is ( n−1 k−1 ) nn−k. 1 ar X iv :0 90 9. 24 00 v1 [ m at h. C O ] 1...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009