From: "Thane Plambeck" thane@best.com
To: "Richard Guy" rkg@cpsc.ucalgary.ca
Subject: Misere Duplicate Kayles
Date: Monday, October 07, 2002 3:19 PM

Hi

In a letter dated 89-12-06 to Conway and cc'ed to Anil Gangolli and myself you included
a draft copy of the Sibert and Conway misere octal game solution for Kayles.

In the cover letter you wrote

"As you say, there's virtually no hope of extending to 2^k-tuple Kayles, but am I wrong
in guessing that only a finite amount of work is needed to include k-plicate Kayles
for k=2, 3,4, ... and k=5/3, 8/3, 11/3, ...."

I've returned to this little topic after a long hiatus.  I hope to have a Mathematica program
that can effectively attack these problems completed in about 1 month's time.  I already
have a program that can quickly verify that a (given) decomposition is correct.

But for now, here is a decomposition for .1377 (Duplicate Kayles) that can be obtained
by eyeballing the Kayles decomposition in the Sibert-Conway paper and, unless I've made 
mistakes in the program, have confirmed is correct:

mzDecompositionPrint[duplicateKaylesDecomp]

PN Positions

{} E{{10, 9}, {7, 8, 2, 1}} D{}
{} E{{34, 33, 24, 23, 18, 17}, {40, 39, 8, 7, 2, 1}} D{}
{50} E{{34, 33, 24, 23, 18, 17}} D{{40, 39, 8, 7, 2, 1}}
{49} E{{34, 33, 24, 23, 18, 17}} D{{40, 39, 8, 7, 2, 1}}

NP Positions

{} E{} D{{10, 9}, {8, 7, 2, 1}}
{} E{{10, 9}} D{{8, 7, 2, 1}}
{} E{{8, 7, 2, 1}} D{{18, 17}}
{24} E{{8, 7, 2, 1}} D{}
{23} E{{8, 7, 2, 1}} D{}
{} E{{34, 33, 24, 23, 18, 17}} D{{40, 39, 8, 7, 2, 1}}
{50} E{} D{{18, 17}, {8, 7, 2, 1}}
{49} E{} D{{18, 17}, {8, 7, 2, 1}}

I hope to have more results soon along these lines.  

Is there anything new in this area that I should be aware of?

Best wishes

Thane

Thane Plambeck
650 321 4884 office
650 323 4928 fax
http://www.plambeck.org.com/home.htm

From: "Richard Guy" rkg@cpsc.ucalgary.ca
To: "Thane Plambeck" thane@best.com
Date: Tuesday, October 08, 2002 6:52 AM

Cc: "Richard Nowakowski" rjn@mathstat.dal.ca 
"Richard Guy" rkg@cpsc.ucalgary.ca; 
"Elwyn Berlekamp" berlek@math.berkeley.edu 
"John Conway" conway@math.princeton.edu 
"David Wolfe" wolfe@gustavus.edu 
"Aviezri Fraenkel" fraenkel@wisdom.weizmann.ac.il

Subject: Re: Misere Duplicate Kayles

Thanks for the message.  This looks promising.
I know of no new results in this area.  R.