Comments on: On Maximal Self-Avoiding Walks http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/ A blog of recreational math and quantum information theory Mon, 06 Feb 2012 21:25:22 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Nathaniel http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/#comment-54 Nathaniel Sat, 23 May 2009 12:39:01 +0000 http://www.nathanieljohnston.com/?p=182#comment-54 Of course! You get your name in the OEIS and a personal "Elithrion was right" post from me, earning you internet accolades from all three readers of my blog ;) Of course! You get your name in the OEIS and a personal “Elithrion was right” post from me, earning you internet accolades from all three readers of my blog ;)

]]> By: Elithrion http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/#comment-53 Elithrion Sat, 23 May 2009 08:19:01 +0000 http://www.nathanieljohnston.com/?p=182#comment-53 You know, your remark about it being impossible makes me want to do it ten times more, of course! I get some sort of accolades if I'm successful, right? You know, your remark about it being impossible makes me want to do it ten times more, of course! I get some sort of accolades if I’m successful, right?

]]> By: Nathaniel http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/#comment-52 Nathaniel Sun, 10 May 2009 16:32:29 +0000 http://www.nathanieljohnston.com/?p=182#comment-52 I am definitely in the group of people who think that finding a general formula for arbitrary k and n isn't realistically possible for this problem as well, which is why I coded those scripts ;) A formula could likely be derived by a very devoted person for the k = 4 and k = 5 cases, but they'd be horrendously long and not particularly informative. I might take another look at the lake counting problem soon, but it still seems to me that as the lakes get bigger and bigger, more and more ways of things "going wrong" crop up, for the most part in rather unpredictable ways, which makes obtaining recurrence relations extremely difficult. The method of relating lakes to polyominoes seems by far the most promising approach so far, so I'll have a look at that again soon, I suppose. I am definitely in the group of people who think that finding a general formula for arbitrary k and n isn’t realistically possible for this problem as well, which is why I coded those scripts ;) A formula could likely be derived by a very devoted person for the k = 4 and k = 5 cases, but they’d be horrendously long and not particularly informative.

I might take another look at the lake counting problem soon, but it still seems to me that as the lakes get bigger and bigger, more and more ways of things “going wrong” crop up, for the most part in rather unpredictable ways, which makes obtaining recurrence relations extremely difficult.

The method of relating lakes to polyominoes seems by far the most promising approach so far, so I’ll have a look at that again soon, I suppose.

]]> By: Elithrion http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/#comment-51 Elithrion Sun, 10 May 2009 15:56:52 +0000 http://www.nathanieljohnston.com/?p=182#comment-51 Some people may disagree about the impossibility of figuring out a general case formula for this as well! Of course, those people should probably put their money where their mouth is and actually attempt to make further progress some time, maybe... Some people may disagree about the impossibility of figuring out a general case formula for this as well! Of course, those people should probably put their money where their mouth is and actually attempt to make further progress some time, maybe…

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