This page contains lists of my publications, including preprints and papers in preparation. Some of these are available from here and others may become available from here in future. Some preprints or papers in preparation may not be listed.

The following are generally excluded from these lists:

- postings to newsgroups, mailing lists and other online discussion fora;
- email or extracts from email or other comments or correspondence not written as formal contributions to correspondence columns but incidentally published online or otherwise;
- incidental quotes or appearances in news or other media;
- bug reports and contributions to bug reports in public bug tracking systems;
- web sites and contributions to web sites (for example, the On-Line Encyclopedia of Integer Sequences and Wikipedia);
- similar online publications using other protocols;
- contributions to free software and documentation;
- any of the above also published in printed books or other forms or media;
- seminars given by someone else based on joint work with me;
- online or printed material privately circulated but not made available to the general public;
- material only receiving public circulation through inclusion in archive collections available to the public.

The following are however included:

- Contributions to refereed online journals or other well-defined online publications (but not simply mailing list messages republished);
- formal defect reports and interpretation requests against technical standards (not drafts);
- other formally identified documents contributed in technical standards development processes;
- formal responses to Government consultations, even when the full set of consultation responses is not published (but not isolated comments on specific issues in such consultations which are not phrased as a full response and are not published).

- Joseph Samuel Myers, Graphs without
Large Complete Minors are Quasi-Random,
Combinatorics, Probability and Computing
**11**(2002), no. 6, 571–585, © 2002 Cambridge University Press.**Abstract**: We answer a question of Sós by showing that, if a graph*G*of order*n*and density*p*has no complete minor larger than would be found in a random graph*G*(*n*,*p*), then*G*is quasi-random, provided either*p*> 0.45631... or κ(*G*) ≥*n*(log log log*n*)/(log log*n*), where 0.45631... is an explicit constant.The results proved can also be used to fill the gaps in an argument of Thomason, describing the extremal graphs having no

*K*_{t}minor for given*t*. - Joseph Samuel Myers, An inequality arising in graph minors, 2001 (online appendix to the previous paper). This appendix serves only to prove an inequality needed in that paper, for which the proof I have involves computation and analysis of many cases; it is of no intrinsic interest.
- Joseph Samuel Myers, The minimum number of monotone
subsequences, The Electronic Journal of Combinatorics
**9(2)**(2002), #R4. (Available as PDF, PostScript or source files (.tar.gz); also accompanying C program.)**Abstract**: Erdős and Szekeres showed that any permutation of length*n*≥*k*^{2}+ 1 contains a monotone subsequence of length*k*+ 1. A simple example shows that there need be no more than such subsequences; we conjecture that this is the minimum number of such subsequences. We prove this for*k*= 2, with a complete characterisation of the extremal permutations. For*k*> 2 and*n*≥*k*(2*k*− 1), we characterise the permutations containing the minimum number of monotone subsequences of length*k*+ 1 subject to the additional constraint that all such subsequences go in the same direction (all ascending or all descending); we show that there are such extremal permutations, where is the*k*^{th}Catalan number. We conjecture, with some supporting computational evidence, that permutations with a minimum number of monotone (*k*+ 1)-subsequences must have all such subsequences in the same direction if*n*≥*k*(2*k*− 1), except for the case of*k*= 3 and*n*= 16. - Joseph Samuel Myers, Extremal Theory of Graph Minors and
Directed Graphs, PhD dissertation,
University of Cambridge, 2003. (Available as PDF or gzipped PostScript; also C program from Appendix A.
The PostScript version is recommended for printing; the PDF version
includes internal and external links.)
**Abstract**: In the first part of this dissertation, the extremal theory of graph minors is developed as follows. The results of Bollobás, Catlin and Erdős showing how large a complete minor is found in a random graph are extended to showing how large a complete bipartite*K*_{s,t}minor is found for given*t*, even up to*t*=*n*− log*n*. The Hadwiger number of random graphs in a model where different parts of the graph have different edge probabilities is determined almost surely. For a class of dense graphs generalising that of complete bipartite graphs, ‘blown-up’ graphs, the extremal problem in terms of average degree is solved asymptotically, generalising results of Thomason, the extremal graphs being random graphs, and it is shown how a restricted class of blown-up graphs are ‘critical’ for this problem. For*K*_{2,t}minors, the extremal problem is solved exactly (rather than asymptotically) with the exact best possible number of edges to force such a minor, the methods being substantially different from those for denser minors. For complete minors, it is shown that the extremal graphs are quasi-random in the sense of Chung, Graham and Wilson, or essentially disjoint unions of quasi-random graphs, answering a question of Sós. The extremal problem in terms of connectivity rather than average degree is also considered, with results that are significantly stronger than those in terms of average degree in the cases where they apply.In the second part of this dissertation, extremal problems relating to directed graphs are considered. The minimum number of monotone subsequences of length

*k*+ 1 in a permutation of length*n*is considered; the extremal permutations are determined exactly for*k*= 2, and for*k*> 2 and*n*≥*k*(2*k*− 1) subject to an additional constraint, the number of extremal permutations being related to the Catalan numbers. - Joseph Samuel Myers, The extremal
function for unbalanced bipartite minors, Discrete
Mathematics
**271**(2003), no. 1–3, 209–222.**Abstract**: We consider the question of what average degree forces a graph to have a*K*_{s,t}minor, for*s*fixed and*t*sufficiently large. In the case of*s*= 2, we show that if*t*is sufficiently large and*G*is a graph with more than ((*t*+ 1) / 2)(|*G*| − 1) edges then*G*has a*K*_{2,t}minor. This result is best possible for |*G*| ≡ 1 (mod*t*). - Joseph Samuel Myers and Andrew Thomason, The extremal function
for noncomplete minors, Combinatorica
**25**(2005), no. 6, 725–753, © 2005 János Bolyai Mathematical Society and Springer-Verlag; the version here is a preprint. The original publication is available at www.springerlink.com for subscribers.**Abstract**: We investigate the maximum number of edges that a graph*G*can have if it does not contain a given graph*H*as a minor (subcontraction). Let*c*(*H*) = inf {*c*:*e*(*G*) ≥*c*|*G*| implies*G*≻*H*}.We define a parameter γ(

*H*) of the graph*H*and show that, if*H*has*t*vertices, thenwhere α = 0.319... is an explicit constant and

*o*(1) denotes a term tending to zero as*t*→ ∞. The extremal graphs are unions of pseudo-random graphs.If

*H*has*t*^{1+τ}edges then , equality holding for almost all*H*and for all regular*H*. We show how γ(*H*) might be evaluated for other graphs*H*also, such as complete multi-partite graphs. - David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim
Goodman-Strauss, An
aperiodic monotile, arXiv:2303.10798 (preprint).
**Abstract**: A longstanding open problem asks for an aperiodic monotile, also known as an “einstein”: a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the “hat” polykite, can form clusters called “metatiles”, for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical—and hence aperiodic—tilings. - David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim
Goodman-Strauss, A chiral
aperiodic monotile, arXiv:2305.17743 (preprint).
**Abstract**: The recently discovered “hat” aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat—the equilateral member of the continuum to which it belongs—is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon’s edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only chiral non-periodic tilings based on a hierarchical substitution system.

- Nathan Sidwell and Joseph Myers, Improving Software Floating Point Support, Proceedings of the GCC Developers’ Summit, June 28th–30th, 2006, Ottawa, Ontario, Canada, 211–218.
- Ryan S. Arnold, Greg Davis, Brian Deitrich, Michael Eager, Emil Medve, Steven J. Munroe, Joseph S. Myers, Steve Papacharalambous, Anmol P. Paralkar, Katherine Stewart and Edmar Wienskoski, Power Architecture® 32-bit Application Binary Interface Supplement 1.0 – Embedded; Power Architecture® 32-bit Application Binary Interface Supplement 1.0 – Linux®; Power Architecture® 32-bit Application Binary Interface Supplement 1.0 – Unified (source code, source code signature; also on github). Power.org, April 19, 2011.
- Joseph Myers, ISO C23 support in the GNU Toolchain, talk given at the GNU Tools Cauldron 2023 (slides).

- Graphs without large complete minors, Combinatorics Seminar, DPMMS, Cambridge, 2001 May 10.

- Appearances in Morgan Matthews and David Brindley (Blast! Films), Beautiful Young Minds, broadcast BBC2, 14 October 2007, 9pm. Rebroadcast BBC4, 6 April 2011, 10:30pm.
- Appearances in Morgan Matthews (Origin Pictures / Minnow Films), X + Y, 2014 (UK cinema release 13 March 2015).

- Eva Myers and Joseph Myers, A Voting Problem,
Eureka
**54**(March 1996), 48–52. - Joseph Myers, Tiling with Regular Star
Polygons, Eureka
**56**(March 2004), 20–27, © 2004 The Archimedeans. An online followup document 2-uniform tilings with regular polygons and regular star polygons (August 2009) is also available. - Max A. Alekseyev, Joseph Samuel Myers, Richard Schroeppel, Scott
R. Shannon, N. J. A. Sloane and Paul Zimmermann, Three Cousins of
Recamán’s Sequence, arXiv:2004.14000
(preprint); Fibonacci Quarterly
**60**(2022), no. 3, 201–219.

- Solution to Problem 1993.6, in Tim Cross, Student
Problems, The Mathematical Gazette
**78**(1994), no. 481 (March 1994), 109–111. Reprinted in Student Problems from The Mathematical Gazette, The Mathematical Association, 2002, 26–28. The original publication is available from JSTOR for subscribers. - Alasdair Kergon and Joseph Myers, Problems Drive 2001 (held by The Archimedeans), 2001 February 18. (The version here incorporates various corrections; for the original version, consult the Archimedeans’ records in the University Archives.)
- Solution to BMO Round 1 Problem 6, in James Cranch and Jenny Gardner, BMO 2006: The British Mathematical Olympiad Rounds 1 & 2: Problems, Solutions and Results, United Kingdom Mathematics Trust, 2006, 24.
- IMO 2019 Shortlisted Problems (editor).

- British Mathematical Olympiad 2005–2006 Round 1 Problem 6 (revision and expansion from 19 December 2005 of a set of solutions originally distributed to markers before the marking weekend).
- International Mathematical Olympiad 2007 Problem 3 (distributed 26 July 2007 to inform coordination of this problem).
- British Mathematical Olympiad 2007–2008 Round 2 Problem 3 (revision and expansion from 19 February 2008 of notes on a generalisation and bounds originally distributed before marking).
- British Mathematical Olympiad 2008–2009 Round 1 Problem 1 (notes updated 31 December 2008 on a generalisation of the problem and associated solution methods and integer sequences).
- Analysis of IMO medal boundary choices; also associated software (available from git://git.ukmt.org.uk/git/medal-boundaries.git with a GitHub mirror).

- Speech in Discussion of the Review of arrangements for voting in University elections and on policy and legislative proposals: Report of the Review Committee, Cambridge University Reporter, no. 5976, 27 October 2004 (vol. 135 no. 4), 138–139.
- Speech in Discussion of the Report of the Council on voting arrangements, Cambridge University Reporter, no. 6027, 15 February 2006 (vol. 136 no. 18), 412–414.
- Speech in Discussion of the Report of the Council on Statutes K, 5 (review) and K, 9 (delegation), Cambridge University Reporter, no. 6049, 18 October 2006 (vol. 137 no. 3), 82.
- Speech in Discussion of the Joint Report of the Council and the General Board on the establishment of a degree of Master of Mathematics and a degree of Master of Advanced Study, Cambridge University Reporter, no. 6138, 28 January 2009 (vol. 139 no. 18), 458.
- Speech in Discussion of the Report of the Council on amendments to Statute A (membership of the Senate and election of student members of the Council), Cambridge University Reporter, no. 6187, 6 May 2010 (vol. 140 no. 28), 797.
- Speech in Discussion of the Report of the Council on the future of the Reporter and other publications, Cambridge University Reporter, no. 6220, 20 April 2011 (vol. 141 no. 24), 676–678.
- Speech in Discussion of the Joint Report of the Council and the General Board on the public display of Class-lists and related matters, Cambridge University Reporter, no. 6430, 15 June 2016 (vol. 146 no. 35), 672–673.
- Speech in Discussion of the Joint Report of the Council and the General Board on the definition of student used in certain procedures applicable to students and in committee membership, Cambridge University Reporter, no. 6493, 31 January 2018 (vol. 148 no. 17), 369.

- Response to consultation paper on the UK implementation of EC Directive 2001/29/EC on the Harmonisation of Certain Aspects of Copyright and Related Rights in the Information Society (EUCD consultation response).

- PASC Interpretation Request P1003.2-157.
- PASC Interpretation Request 1003.2-92 #176. (No official response before the standard was obsoleted; last status.)
- Open Group Single UNIX Specification Defect Report OGspecs 212.
- Austin Group Technical Reviewer and Austin Group Working Group Member for the development of IEEE Std 1003.1-2001 (Standard for Information Technology—Portable Operating System Interface (POSIX®)) (also Open Group Base Specifications, Issue 6).
- A defect report in this standard.
- ISO C Defect Reports, proposed wording and associated discussions: WG14 documents N1099, N1100, N1101, N1102, N1103, N1104, N1105, N1220, N1221, N1222, N1223, N1224, N1237, N1238, N1239, N1259, N1260, N1730, N1731; the BSI comments in N1553; comments in N1618; a comment in N1702; N1742; the comments in N1770; comments in N1804; the comment in N1815; the comments in N1854; the comments in N1855; N2173; N2174; N2958; most of the UK comments in N3067; N3070; N3071.

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Contact: Joseph Myers (jsm@polyomino.org.uk)

Last updated: 12 October 2023