Unions and Intersections of Leray Complexes
نویسندگان
چکیده
A simplicial complex X is d-Leray if H̃i(Y ;Q) = 0 for all induced subcomplexes Y ⊂ X and i ≥ d. Let L(X) denote the minimal d such that X is d-Leray. Theorem: Let X,Y be simplicial complexes on the same vertex set. Then L(X ∩ Y ) ≤ L(X) + L(Y ) , L(X ∪ Y ) ≤ L(X) + L(Y ) + 1 .
منابع مشابه
Intersections of Leray complexes and regularity of monomial ideals
For a simplicial complex X and a field K, let h̃i(X) = dim H̃i(X;K). It is shown that if X,Y are complexes on the same vertex set, then for k ≥ 0 h̃k−1(X ∩ Y ) ≤ ∑
متن کاملIntersection patterns of convex sets via simplicial complexes, a survey
The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called d-representable, d-collapsible and d-Leray simplicial complexes which are very useful for this study. We study the differences among these notions and we also focus ...
متن کاملSound and Complete Flow Typing with Unions, Intersections and Negations
Flow typing is becoming a popular mechanism for typing existing programs written in untyped languages (e.g. JavaScript, Racket, Groovy). Such systems require intersections for the true-branch of a type test, negations for the false-branch, and unions to capture the flow of information at meet points. Type systems involving unions, intersections and negations require a subtype operator which is ...
متن کاملE ective Randomness of Unions and Intersections
We investigate the -randomness of unions and intersections of random sets under various notions of randomness corresponding to di erent probability measures. For example, the union of two relatively MartinL of random sets is not Martin-L of random but is random with respect to the Bernoulli measure 3 4 under which any number belongs to the set with probability 3 4 . Conversely, any 3 4 random...
متن کاملCompressed bitmap indexes: beyond unions and intersections
Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND,OR, NOT) that are ideally suited for bitmaps. However, it is less obvious how to apply bitmaps to more advanced queries. For example, we might seek products in a store that meet some, but maybe not a...
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 2005