Multiscale shape equivalence

1996 ◽  
Author(s):  
Peter Forte ◽  
Darrel Greenhill
Keyword(s):  
Shape Equivalence

scholarly journals CE equivalence and shape equivalence of 1-dimensional compacta

1987 ◽  
Vol 26 (2) ◽  
pp. 131-142 ◽  
Author(s):  
R.J. Daverman ◽  
G.A. Venema
Keyword(s):  
Shape Equivalence

scholarly journals Covariant Functors and Shapes in the Category of Compacts

2019 ◽  
Vol 65 (1) ◽  
pp. 21-32
Author(s):  
T F Zhuraev ◽  
Z O Tursunova ◽  
K R Zhuvonov
Keyword(s):  
Compact Space ◽  
Connected Components ◽  
Probability Measures ◽  
Compact Sets ◽  
Shape Preserving ◽  
Shape Equivalence

In this paper, we consider covariant functors F : Comp → Comp acting in category of shape-preserving compact sets [2], infinite compact sets, and shape equivalence [9]. Also we study action of compact functors and shape properties of the compact space X consisting of connected components ОX of the compact X as well as shape identity ShX = ShY of infinite compacts X and Y for the space P (X) of probability measures and its subspaces.

scholarly journals Beyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux

10.37236/3246 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Nihal Gowravaram ◽  
Ravi Jagadeesan
Keyword(s):  
Pattern Avoidance ◽  
General Context ◽  
Young Tableaux ◽  
Young Diagrams ◽  
Alternating Permutations ◽  
Equivalence Type ◽  
Shape Equivalence ◽  
Pattern Avoiding Permutations ◽  
Wilf Equivalence

We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf equivalence to apply to alternating permutations and so generalize results of Backelin-West-Xin and Ouchterlony to alternating permutations. Second, we study pattern avoidance in the more general context of permutations with restricted ascents and descents. We consider a question of Lewis regarding permutations that are the reading words of thickened staircase Young tableaux, that is, permutations that have $k-1$ ascents followed by a descent, followed by $k-1$ ascents, et cetera. We determine the relative sizes of the sets of pattern-avoiding $(k-1)$-ascent permutations in terms of the forbidden pattern. Furthermore, inequalities in the sizes of sets of pattern-avoiding permutations in this context arise from further extensions of shape-equivalence type enumerations. This paper is the first of a two-paper series presenting the work of Beyond alternating permutations: Pattern avoidance in Young diagrams and tableaux (arXiv:1301.6796v1). The second in the series is Ascent-descent Young diagrams and pattern avoidance in alternating permutations (by the second author, submitted).

scholarly journals Shape equivalence under perspective and projective transformations

1997 ◽  
Vol 4 (2) ◽  
pp. 248-253 ◽  
Author(s):  
Johan Wagemans ◽  
Christian Lamote ◽  
Luc Van Gool
Keyword(s):  
Projective Transformations ◽  
Shape Equivalence

Shape Equivalences of Whitney Continua of Curves

1988 ◽  
Vol 40 (1) ◽  
pp. 217-227 ◽  
Author(s):  
Hisao Kato
Keyword(s):  
Metric Space ◽  
Hausdorff Metric ◽  
Compact Metric Space ◽  
Monotone Map ◽  
Shape Equivalence ◽  
Image Position

By a compactum, we mean a compact metric space. A continuum is a connected compactum. A curve is a 1-dimensional continuum. Let X be a continuum and let C(X) be the hyperspace of (nonempty) subcontinua of X, C(X) is metrized with the Hausdorff metric (e.g., see [12] or [18]). One of the most convenient tools in order to study the structure of C(X) is a monotone map ω:C(X) → [0, ω(X)] defined by H. Whitney [25]. A map ω:C(X) → [0, ω(X)] is said to be a Whitney map for C(X) provided thatThe continua {ω−1} (0 < t < ω(X)) are called the Whitney continua of X. We may think of the map ω as measuring the size of a continuum. Note that ω−1(0) is homeomorphic to X and ω−1(ω(X)) = {X}. Naturally, we are interested in the structures of ω−1(t)(0 < t < ω(X)). In [14], J. Krasinkiewicz proved that if X is a circle-like continuum and ω is any Whitney map for C(X), then for any 0 < t < ω(X)ω−1(t) is shape equivalent to X, i.e., Sh ω−1(t) = Sh X (e.g., see [1] or [17]). In [8], we proved the following: If one of the conditions (i) and (ii) is satisfied, then the shape morphismwhich is defined in [7] and [8], is a shape equivalence.

Sign in / Sign up

Export Citation Format

Share Document