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Some Articles J.L.F. King
Most files are compressed and, unless otherwise mentioned,
are in postscript.
Some of the articles below are also listed on the
Tiling
Page.
A brief file gives short
abstracts (pdf)
of some of the following articles.
If your site subscribes to Mathematical Reviews, then you can
read MR reviews of
some of my articles electronically.
You can obtain a
list of the citations,
in BibTeX format,
should you wish to cite one of my articles in one of yours.
 24

23 July 2001:
Flat stacks, JoiningClosure and Genericity (pdf).
This shows that for the generic transformation, the set of offdiagonal
joinings is dense in the simplex of all joinings. Thus it generalizes the
conclusion of the Weakclosure theorem, by weakening the hypothesis from
rank1 to simply a residual subset of the flat stacks
maps.
 29

24 June 1998
deBruijn's
Harmonic Brick Condition is computable
(pdf, 6 pages),
will appear in the Electronic Journal of Combinatorics.
The article has two figures. Figure E4 is also available separately
as a
jpeg file.
The article shows the following: Given N integersided bricks, each of
dimension D (the protobricks), when is it the case that each box
which is packable by translates of copies of protobricks, in fact can be
"parallel packed" by copies of a single protobrick?
Protobricks for which the answer is yes
I call a deBruijn brickset.
My article gives an algorithm to detect when a brickset
is deBruijn. The algorithm runs in time big O
of DN^{3}.
The article ends with two open questions.
Articles 04 and 05 are not yet available electronically, but I do have
paper reprints of them. Please
contact me
if you would like copies.
 01

A counterexample to a positive entropy skew product generalization
of the Pinsker Conjecture
appeared in
Ergodic Theory & Dynamical Systems
in 1985.
 02

27 Sep 1998
In order to enhance the connections between diagrams in
The commutant is the weakclosure of the powers, for rank1 transformations
(pdf, 23 pages),
I have judiciously used color on certain ingredients. The original version of
the article
appeared, in 1986, in
Ergodic Theory & Dyn.Sys.
vol. 6, (1986), 363–384.
 03

For mixing transformations
rank( T^{k} )
=
k
·
rank( T)
(pdf, 14 pages),
appeared, also in 1986, in the
Israel Journal of Mathematics.
While, the PDF file does not have the three figures,
these figures are available
available separately,
in magnified format, as GIF files:
Figure 15,
Figure 21 and
Figure 23.
 04

An invariant for rank1 rigid transformations
appeared in
Ergodic Theory & Dyn. Sys.
in 1988.
 05

Joiningrank and the structure of finite rank mixing transformations
appeared, in 1991, in
Jour. d'Analyse Mathématiques.
Its sequel is article 12, below.
 06

A lower bound on the rank of mixing extensions
(pdf, 3 pages),
appeared in
Israel Jour. Math..
 07

A group rotation factor of a nonrigid rank1 map
(13 pages),
appeared as the volume
Dynamical Systems (Proceedings, U. of Maryland).
in Springer Lecture Notes in Mathematics, #1342.
The article's two figures are included, and are also available separately
as GIF files:
Figure 3.8 and
Figure 3.12.
 08

Lightly mixing is closed under countable products
(pdf, 5 pages),
appeared in
Israel Jour. Math..
 09

An obstruction to Kfold splitting
(pdf, 4 pages),
appeared in the volume of the AMS
Contemporary Mathematics
in honor of Dorothy Maharam Stone.
 10

A map with topological minimal selfjoinings
in the sense of del Junco
(pdf, 16 pages),
appeared in
Ergodic Theory & Dyn. Sys..
 11

Closure properties of the class of Uniform Sweepingout
transformations (pdf, 4 pages), appeared in
Illinois J. Math..
 12

A canonical structure theorem for finite joiningrank maps
(pdf, 18 pages),
appeared in
Jour. d'Analyse Mathématiques.
This is a sequel to
Joiningrank and the structure…,
which is reference 5, above.
 13
 A paper on multiple mixing, disjointness, and joinings,
Ergodic properties where order 4 implies infinite order
(pdf, 21 pages),
appeared in a shorter form in the
Israel Jour. Math.
 15
 Unfortunately, the figures for
Rank One Lightly Mixing
(7 pages),
are not currently available.
Here, Friedman and I construct a lightly mixing map which is not
partially mixing. It appeared in the
Israel Jour. Math..
All figures are included in the article. One large figure is are also
available separately as a GIF file:
Figure 3.1.
 16

Dilemma of the Sleeping Stockbroker
(4 pages)
appeared in
The Amer. Math. Monthly.
 17

Three Problems in search of a Measure
(pdf, 19 pages)
won a
Lester R. Ford Award
for mathematical exposition. The article appears in the 1994 issue of
The Amer. Math. Monthly with the cover drawing of Bernoulli.
2 Aug 1997:
The Board of Governors of the MAA awarded this article
The Merten M. Hasse Prize,
at the Atlanta Mathfest.
 18
 A companion article to the above is a 1995
Mathematical Intelligencer paper,
Billiards inside a cusp
(pdf, 14 pages)
 19
 The Stockbroker Problem was taken up again in
A countablyvalued Sleeping Stockbroker Process
(pdf, 5 pages),
written with Steve Kalikow. This appeared in vol. 7 of the
Jour. of Theoretical Probability, in 1994.
 20
 Mustafa Akcoglu and I produced
An example of pointwise nonconvergence of
Iterated Conditional Expectation Operators
(7 pages).
It appeared in the
Israel Jour Math in 1996.
The article's one figure (large) is also available as a separate GIF file:
Figure 3.
 21
 For those of you who asked,
An answer to M. Gordin's homoclinic question
is in the March 1997 issue of the
International Mathematics Research Notices.
(8 pages)
 22

In
Shape Tiling
(6 pages),
Kevin Keating and I examined tiling rectangles with other rectangles.
It appeared in the Electronic Journal of Combinatorics, in the
special 1997 issue in honor of Prof. Herb Wilf, and this
version
is available in several formats.
 23

8 Dec 1996:
Eli Glasner and I prove
A zeroone law for dynamical properties
(PDF, 12 pages).
We also establish a Baire/meager/residual equivalence between two of the
standard topologies on dynamical systems.
This appeared
(09Jan1998)
in vol. 215 of
Contemporary Mathematics: Topological Dynamics and Applications,
the volume in honor of Robert Ellis.
The XXX Math Archives has a
version
which is available in PS, PDF, DVI and other formats.
 25

3 Nov 1997:
Continuing from Shape Tiling,
Kevin and I again look at rectangular tilings in
Signed Tilings with Squares
(8 pages),
this time using a tensor product to studying tilings of
weighted rectangular regions, W, in the plane. We
obtain an ifandonlyif condition for whether W
can be Ztiling by rectangles of specified eccentricities.
It appeared in the
Jour. of Combinatorial Theory, Series A
85, (1999) 8391.
 26

08 June 1998 (Updated 23Jun1998):
A changeofcoordinates from Geometry to Algebra,
applied to Brick Tilings
(18 pages) has appeared in the
Proceedings from the First International Conference
on Semigroups & Algebraic Engineering
(Proceedings)
The conference was held in AizuWakamatsu City, Japan, during
March 2428 of 1997.
This is a preparatory paper
for proving the Polynomial Conjecture of …Monotone Boolean Functions
(on Tilings Page),
and describes the transition from the Geometry to the Lattice Theory in a
series of steps. The technical proofs of these steps will appear elsewhere.
The XXX Math Archives has a
version
which is available in PS, PDF, DVI and other formats.
 34

14 Feb 2000:
In memory of Anzelm Iwanik there was a special volume of
Colloquium Mathematicum. My article for this memorial volume,
The generic transformation has roots of all orders
,
(pdf)
has recently appeared.
The article shows, under the usual course topology on the space of
measurepreserving transformations, that there is a residual
(Baire category fat)
collection of transformations which have a squareroot, a cuberoot etc.
The above PDF version is an expanded version of the published article,
having an openquestion section at the end. However, it is missing
the bibliography of the published article.
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