Search results for "combinatoric"
showing 10 items of 1776 documents
ON THE INDEX OF VECTOR FIELDS TANGENT TO HYPERSURFACES WITH NON-ISOLATED SINGULARITIES
2002
Let $F$ be a germ of a holomorphic function at $0$ in ${\bb C}^{n+1}$ , having $0$ as a critical point not necessarily isolated, and let $\tilde{X}:= \sum^n_{j=0} X^j(\partial/\partial z_j)$ be a germ of a holomorphic vector field at $0$ in ${\bb C}^{n+1}$ with an isolated zero at $0$ , and tangent to $V := F^{-1}(0)$ . Consider the ${\cal O}_{V,0}$ -complex obtained by contracting the germs of Kahler differential forms of $V$ at $0$ \renewcommand{\theequation}{0.\arabic{equation}} \begin{equation} \Omega^i_{V,0}:=\frac{\Omega^i_{{\bb C}^{n+1},0}}{F\Omega^i_{{\bb C}^{n+1},0}+dF\wedge{\Omega^{i-1}}_{{\bb C}^{n+1}},0} \end{equation} with the vector field $X:=\tilde{X}|_V$ on $V$ : \begin{equa…
On Fine and Wilf's theorem for bidimensional words
2003
AbstractGeneralizations of Fine and Wilf's Periodicity Theorem are obtained for the case of bidimensional words using geometric arguments. The domains considered constitute a large class of convex subsets of R2 which include most parallelograms. A complete discussion is provided for the parallelogram case.
Two shortest path metrics on well-formed parentheses strings
1996
We present an analysis of two transformations on well-formed parentheses strings. Using a lattice approach, the corresponding least-move distances are computable, the first in linear time and the second in quadratic time.
Hausdorff measures, Hölder continuous maps and self-similar fractals
1993
Let f: A → ℝn be Hölder continuous with exponent α, 0 < α ≼ 1, where A ⊂ ℝm has finite m-dimensional Lebesgue measure. Then, as is easy to see and well-known, the s-dimensional Hausdorif measure HS(fA) is finite for s = m/α. Many fractal-type sets fA also have positive Hs measure. This is so for example if m = 1 and f is a natural parametrization of the Koch snow flake curve in ℝ2. Then s = log 4/log 3 and α = log 3/log 4. In this paper we study the question of what s-dimensional sets in can intersect some image fA in a set of positive Hs measure where A ⊂ ℝm and f: A → ℝn is (m/s)-Hölder continuous. In Theorem 3·3 we give a general density result for such Holder surfacesfA which implies…
4-Manifold topology I: Subexponential groups
1995
The technical lemma underlying the 5-dimensional topological s-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ~-null immersions of disks. These conjectures are theorems precisely for those fundamental groups ("good groups") where the ~l-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two opera- tions: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.
On Banaschewski functions in lattices
1991
hold for all x, y ~ X. We call such a function z a Banaschewski function or a B-function on X. A lattice L is a B-lattice or antitonely complemented, if there is a B-function defined on the whole lattice L. For instance, Boolean lattices as well as orthocomplemented lattices are B-lattices. On the other hand, a B-lattice is not necessarily Boolean or orthocomplemented, although a distributive B-lattice is a Boolean lattice. It is shown later that a matroid (geometric) lattice is also a B-lattice. Naturally, our results include the lemma of Banaschewski [ 1, Lemma 4], by which the lattice of the subspaces of a vector space is a B-lattice. It should be emphasized that a B-function is supposed…
Size of Sets with Small Sensitivity: A Generalization of Simon’s Lemma
2015
We study the structure of sets \(S\subseteq \{0, 1\}^n\) with small sensitivity. The well-known Simon’s lemma says that any \(S\subseteq \{0, 1\}^n\) of sensitivity \(s\) must be of size at least \(2^{n-s}\). This result has been useful for proving lower bounds on the sensitivity of Boolean functions, with applications to the theory of parallel computing and the “sensitivity vs. block sensitivity” conjecture.
Operators on PIP-Spaces and Indexed PIP-Spaces
2009
As already mentioned, the basic idea of pip-spaces is that vectors should not be considered individually, but only in terms of the subspaces V r (r Є F), the building blocks of the structure. Correspondingly, an operator on a pipspace should be defined in terms of assaying subspaces only, with the proviso that only continuous or bounded operators are allowed. Thus an operator is a coherent collection of continuous operators. We recall that in a nondegenerate pip-space, every assaying subspace V r carries its Mackey topology \(\tau (V_r , V \bar{r})\) and thus its dual is \(V \bar{r}\). This applies in particular to \(V^{\#}\) and V itself. For simplicity, a continuous linear map between two…
Foliations, Lineations and Lattice Preferred Orientation
1998
Many microstructures in rocks are defined by a preferred orientation of minerals or fabric elements. We distinguish foliations, lineations and lattice-preferred orientation.
Classifiers in Sinitic languages: From individuation to definiteness-marking
2012
Abstract This article examines the distribution and interpretation of the bare classifier phrase [Cl+N] in three Sinitic languages of Mandarin, Wu and Cantonese. We show that [Cl+N] can be interpreted as definite or indefinite depending on pragmatic factors related to information structure and word order. Syntactically, we claim that indefinite [Cl+N] has the maximal projection of ClP and that definite [Cl+N] is a DP, where the D head is filled by the classifier via Cl-to-D raising. Semantically, we claim that indefinite [Cl+N] is predicative, denoting sets of atomic entities and that definite [Cl+N] is derived from indefinite [Cl+N] by lifting it from predicates to Generalized Quantifiers.…