scholarly journals On the order dimension of locally countable partial orderings

2020 ◽  
Vol 148 (7) ◽  
pp. 2823-2833 ◽  
Author(s):  
Kojiro Higuchi ◽  
Steffen Lempp ◽  
Dilip Raghavan ◽  
Frank Stephan
Keyword(s):  
Order Dimension ◽  
Locally Countable ◽  
Partial Orderings

Partial Orderings on Con-S-K-Ep Matrices

2012 ◽  
Vol 3 (8) ◽  
pp. 1-6
Author(s):  
Dr. G.Ramesh Dr. G.Ramesh ◽  
◽  
Dr. B.K.N.Muthugobal Dr. B.K.N.Muthugobal
Keyword(s):  
Partial Orderings

Babbitt’s Beguiling Surfaces, Improvised Inside; Part III: Opportunities

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
Joshua Banks Mailman
Keyword(s):  
Music Composition ◽  
Jazz Improvisation ◽  
The Third ◽  
Partial Orderings ◽  
Compositional Structures ◽  
Surface Patterns ◽  
Inside Part ◽  
Musical Activities

Babbitt’s relatively early composition Semi-Simple Variations (1956) presents intriguing surface patterns that are not determined by its pre-compositional plan, but rather result from subsequent “improvised” decisions that are strategic. This video (the third of a three-part video essay) considers Babbitt’s own conversational pronouncements (in radio interviews) together with some particulars of his life-long musical activities, that together suggest uncanny affiliations to jazz improvisation. As a result of Babbitt’s creative reconceptualizing of planning and spontaneity in music, his pre-compositional structures (partial orderings) fit in an unexpected way into (or reformulate) the ecosystem relating music composition to the physical means of its performance.

scholarly journals The order dimension of divisibility

2021 ◽  
Vol 179 ◽  
pp. 105391
Author(s):  
David Lewis ◽  
Victor Souza
Keyword(s):  
Order Dimension

scholarly journals Left-star and right-star partial orderings

1991 ◽  
Vol 149 ◽  
pp. 73-89 ◽  
Author(s):  
Jerzy K. Baksalary ◽  
Sujit Kumar Mitra
Keyword(s):  
Partial Orderings

scholarly journals Dynamical effects of partial orderings in physical systems

1996 ◽  
Vol 54 (4) ◽  
pp. 3135-3141 ◽  
Author(s):  
A. S. Landsberg ◽  
Eric J. Friedman
Keyword(s):  
Physical Systems ◽  
Partial Orderings

On countably compact, locally countable spaces

1979 ◽  
Vol 10 (2-3) ◽  
pp. 193-206 ◽  
Author(s):  
I. Juhász ◽  
Zs. Nagy ◽  
W. Weiss
Keyword(s):  
Countably Compact ◽  
Locally Countable

Natural Partial Orders

1968 ◽  
Vol 20 ◽  
pp. 535-554 ◽  
Author(s):  
R. A. Dean ◽  
Gordon Keller
Keyword(s):  
Partial Orders ◽  
Partial Ordering ◽  
Finite Set ◽  
Partial Orderings

Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering. This is a consequence of the theorem of Szpielrajn (5) which states that every partial ordering of a set may be refined to a total ordering. In this paper we consider only natural partial orderings. In the first section we obtain theorems about the lattice of all NPO's of T(n).

Stochastic ordering of random processes with an imbedded point process

1991 ◽  
Vol 28 (3) ◽  
pp. 553-567 ◽  
Author(s):  
François Baccelli
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Random Sequence ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Time Process ◽  
Continuous Time Process ◽  
Partial Orderings ◽  
Stationary Probabilities

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

An AD-like model

1985 ◽  
Vol 50 (2) ◽  
pp. 531-543 ◽  
Author(s):  
Arthur W. Apter
Keyword(s):  
Measurable Cardinal ◽  
Large Cardinals ◽  
Strong Sense ◽  
Supercompact Cardinals ◽  
Singular Cardinals ◽  
Partial Orderings ◽  
Measurable Cardinals ◽  
Jonsson Cardinals

A very fruitful line of research in recent years has been the application of techniques in large cardinals and forcing to the production of models in which certain consequences of the axiom of determinateness (AD) are true or in which certain “AD-like” consequences are true. Numerous results have been published on this subject, among them the papers of Bull and Kleinberg [4], Bull [3], Woodin [15], Mitchell [11], and [1], [2].Another such model will be constructed in this paper. Specifically, the following theorem is proven.Theorem 1. Con(ZFC + There are cardinals κ < δ < λ so that κ is a supercompact limit of supercompact cardinals, λ is a measurable cardinal, and δ is λ supercompact) ⇒ Con(ZF + ℵ1 and ℵ2 are Ramsey cardinals + The ℵn for 3 ≤ n ≤ ω are singular cardinals of cofinality ω each of which carries a Rowbottom filter + ℵω + 1 is a Ramsey cardinal + ℵω + 2 is a measurable cardinal).It is well known that under AD + DC, ℵ2 and ℵ2 are measurable cardinals, the ℵn for 3 ≤ n < ω are singular Jonsson cardinals of cofinality ℵ2, ℵω is a Rowbottom cardinal, and ℵω + 1 and ℵω + 2 are measurable cardinals.The proof of the above theorem will use the existence of normal ultrafilters which satisfy a certain property (*) (to be defined later) and an automorphism argument which draws upon the techniques developed in [9], [2], and [4] but which shows in addition that certain supercompact Prikry partial orderings are in a strong sense “homogeneous”. Before beginning the proof of the theorem, however, we briefly mention some preliminaries.

scholarly journals Tight Quotients and Double Quotients in the Bruhat Order

10.37236/1871 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
John R. Stembridge
Keyword(s):  
Coxeter Groups ◽  
Upper Bounds ◽  
Bruhat Order ◽  
Weyl Groups ◽  
Order Dimension ◽  
Parabolic Subgroups ◽  
Affine Weyl Groups ◽  
Positive Side ◽  
Maximal Parabolic Subgroups

It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic subgroups. Similarly, the Bruhat order is also the conjunction of a larger number of simpler quotients obtained by projecting onto two-sided (i.e., "double") quotients by pairs of maximal parabolic subgroups. Each one-sided quotient may be represented as an orbit in the reflection representation, and each double quotient corresponds to the portion of an orbit on the positive side of certain hyperplanes. In some cases, these orbit representations are "tight" in the sense that the root system induces an ordering on the orbit that yields effective coordinates for the Bruhat order, and hence also provides upper bounds for the order dimension. In this paper, we (1) provide a general characterization of tightness for one-sided quotients, (2) classify all tight one-sided quotients of finite Coxeter groups, and (3) classify all tight double quotients of affine Weyl groups.

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