From chandan1788@gmail.com Wed Apr 13 12:15:32 2011 Received: from nomail.cs.rutgers.edu (nomail.cs.rutgers.edu [128.6.168.251]) by math.rutgers.edu (8.11.7p3+Sun/8.8.8) with ESMTP id p3DGFVx28577 for ; Wed, 13 Apr 2011 12:15:31 -0400 (EDT) X-Virus-Scanned: by nomail-cgpav-clamav-v1.3b Received: by nomail.cs.rutgers.edu (CommuniGate Pro PIPE 5.3.7 _community_) with PIPE id 9924713; Wed, 13 Apr 2011 12:15:12 -0400 X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on spamfilter1.rutgers.edu X-Spam-ASN: AS15169 209.85.128.0/17 X-Spam-Status: No, score=0.3 required=5.0 tests=BAYES_00,BOTNET_SERVERWORDS, DKIM_SIGNED,DKIM_VALID,DKIM_VALID_AU,DKIM_VERIFIED,FREEMAIL_ENVFROM_END_DIGIT, FREEMAIL_FROM,HTML_MESSAGE,RCVD_IN_DNSWL_NONE,RELAYCOUNTRY_US,SPF_PASS shortcircuit=no autolearn=disabled version=3.3.1 X-Spam-Relay-Country: US X-Spam-Language: en X-Spam-Level: Received: from mail-qw0-f47.google.com ([209.85.216.47] verified) by nomail.cs.rutgers.edu (CommuniGate Pro SMTP 5.3.7 _community_) with ESMTPS id 9924708 for zeilberg@math.rutgers.edu; Wed, 13 Apr 2011 12:14:55 -0400 Received: by qwh5 with SMTP id 5so486507qwh.20 for ; Wed, 13 Apr 2011 09:14:40 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:in-reply-to:references:date :message-id:subject:from:to:content-type; bh=gFrVozFSBt+izjurnN5x56eUyrqapj9Z4nPnAtbK2AA=; b=Fzd9Cv8h6s2ErBoDFe0DDcHLM5mE2OAJgD4KpbXepwMeepU65/xOdP+BTlX7V4dTut l2dz3bJmhnzRbbJm2M8Rzlzh8IJ3KpZ5eyf2uenJ4RUwEtLdG/VRevx8Bkn8ZgPmcCsq aX6s+5xKd23Ii0Cfx82hKmWVuM4yUAQMSl1xE= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type; b=aGyW7+dVFb4JGHZJiXW8MCL6w/kpB9NptcoTvDFgwO3QsOwOwCcFXpvyq7WAOqMfzz WR94+1Bpjavk1hJrthL64iHLXQ38xG2tPVyNJifrRbDB23D1ZrbNB6oPRRL9iqpPXtKl g+c/tNu1CKs2Wd+ozrROlTCSYNtxlc+h4R4wQ= MIME-Version: 1.0 Received: by 10.229.88.197 with SMTP id b5mr6280772qcm.226.1302711280463; Wed, 13 Apr 2011 09:14:40 -0700 (PDT) Received: by 10.229.245.144 with HTTP; Wed, 13 Apr 2011 09:14:40 -0700 (PDT) In-Reply-To: <201104061228.p36CSJk24240@math.rutgers.edu> References: <201104061228.p36CSJk24240@math.rutgers.edu> Date: Wed, 13 Apr 2011 21:44:40 +0530 Message-ID: Subject: Re: Help required in combinatorics. MathIsFun From: Chandan Jha To: Doron Zeilberger Content-Type: multipart/alternative; boundary=001636426e0f1df32404a0cf1b82 Status: R Content-Length: 2750 --001636426e0f1df32404a0cf1b82 Content-Type: text/plain; charset=ISO-8859-1 Dear Doron, This field seems to be very interesting and I would be very grateful to you if you could tell me about the applicability of ternary square-free numbers or the connective constant. Is this only of theoretical interest or there are some areas where it finds its usage. I will continue working in this field to see whether I can come up with some improvements to the work already done in this field. Please reply telling me about the applicability. Thanking you. Regards, Chandan. On Wed, Apr 6, 2011 at 5:58 PM, Doron Zeilberger wrote: > Dear Mr. Chandan Kumar Jha, > > Thanks for your interest. The question is still wide open. It is possible > that with more > computing powers, one should be able to improve Grimm's current lower > bound, but it is > still far from what is believed to be the exact answer. The exact answer is > probably > closer to the currently known upper bound, but no one knows how to get > there. > You are welcome to try! > > Best wises > > Doron Zeilberger > > --001636426e0f1df32404a0cf1b82 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Dear Doron,

This field seems to be very interesting and I would be= =20 very grateful to you if you could tell me about the applicability of=20 ternary square-free numbers or the connective constant. Is this only of=20 theoretical interest or there are some areas where it finds its usage. I=20 will continue working in this field to see whether I can come up with=20 some improvements to the work already done in this field. Please reply tell= ing me about the=20 applicability. Thanking you.

Regards,
Chandan.

On Wed, Apr 6, 2011 at 5:58 PM, Doron Zeilberger <zeilberg@math.rut= gers.edu> wrote:
Dear Mr. Chandan = Kumar Jha,

=A0Thanks for your interest. The question is still wide open. It is possib= le that with more
computing powers, one should be able to improve Grimm's current lower b= ound, but it is
still far from what is believed to be the exact answer. The exact answer is= probably
closer to the currently known upper bound, but no one knows how to get ther= e.
=A0You are welcome to try!

=A0 =A0Best wises

=A0 =A0 =A0 =A0Doron Zeilberger


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