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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 PageTilings 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.



23 July 2001:     Flat stacks, Joining-Closure and Genericity (pdf).

This shows that for the generic transformation, the set of off-diagonal joinings is dense in the simplex of all joinings. Thus it generalizes the conclusion of the Weak-closure theorem, by weakening the hypothesis from rank-1 to simply a residual subset of the flat stacks maps.

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 integer-sided 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 brick-set. My article gives an algorithm to detect when a brick-set is deBruijn. The algorithm runs in time big O of DN3. The article ends with two open questions.

Published articles

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.

A counterexample to a positive entropy skew product generalization of the Pinsker Conjecture appeared in Ergodic Theory & Dynamical Systems in 1985.
27 Sep 1998     In order to enhance the connections between diagrams in The commutant is the weak-closure of the powers, for rank-1 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.
For mixing transformations rank( Tk ) = 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.
An invariant for rank-1 rigid transformations appeared in Ergodic Theory & Dyn. Sys. in 1988.
Joining-rank and the structure of finite rank mixing transformations appeared, in 1991, in Jour. d'Analyse Mathématiques. Its sequel is article 12, below.
A lower bound on the rank of mixing extensions (pdf, 3 pages), appeared in Israel Jour. Math..
A group rotation factor of a non-rigid rank-1 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.
Lightly mixing is closed under countable products (pdf, 5 pages), appeared in Israel Jour. Math..
An obstruction to K-fold splitting (pdf, 4 pages), appeared in the volume of the AMS Contemporary Mathematics in honor of Dorothy Maharam Stone.
A map with topological minimal self-joinings in the sense of del Junco (pdf, 16 pages), appeared in Ergodic Theory & Dyn. Sys..
Closure properties of the class of Uniform Sweeping-out transformations (pdf, 4 pages), appeared in Illinois J. Math..
A canonical structure theorem for finite joining-rank maps (pdf, 18 pages), appeared in Jour. d'Analyse Mathématiques. This is a sequel to Joining-rank and the structure…, which is reference 5, above.
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.
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.

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

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.

A companion article to the above is a 1995 Mathematical Intelligencer paper, Billiards inside a cusp (pdf, 14 pages)
The Stockbroker Problem was taken up again in A countably-valued Sleeping Stockbroker Process (pdf, 5 pages), written with Steve Kalikow. This appeared in vol. 7 of the Jour. of Theoretical Probability, in 1994.
Mustafa Akcoglu and I produced An example of pointwise non-convergence 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.
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)
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.
8 Dec 1996: Eli Glasner and I prove A zero-one 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.

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 if-and-only-if condition for whether W can be Z-tiling by rectangles of specified eccentricities.

It appeared in the Jour. of Combinatorial Theory, Series A 85, (1999) 83-91.


08 June 1998 (Updated 23Jun1998): A change-of-coordinates 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 Aizu-Wakamatsu City, Japan, during March 24-28 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.


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 measure-preserving transformations, that there is a residual (Baire category fat) collection of transformations which have a square-root, a cube-root etc.

The above PDF version is an expanded version of the published article, having an open-question section at the end. However, it is missing the bibliography of the published article.

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