Special whole numbers... - Page 41

Dr Sardonicus · 2020-10-17, 21:55

Quote:

Originally Posted by Viliam Furik

Well, it's then either the fact it's the smallest non-supersingular prime, or that it is the mirror of Sheldon prime (73). I guess you meant the former.

You guess correctly. Go to the head of the class!

Your offering 3,560,600,696,674 has AFAIK defied analysis so far (I haven't figured out why it is special), so you're current.

Viliam Furik · 2020-10-17, 23:32

Quote:

Originally Posted by Dr Sardonicus

You guess correctly. Go to the head of the class!

Your offering 3,560,600,696,674 has AFAIK defied analysis so far (I haven't figured out why it is special), so you're current.

I can give a few hints:

1. It is a sum of a part of an infinite series of numbers
2. The series is related to the graph theory

mart_r · 2020-11-01, 10:37

Hmm... I wanted to post a new number, but still can't figure out Viliam Furik's number.
And I don't know much about graph theory either.

Dr Sardonicus · 2020-11-01, 21:46

I'm afraid the hints haven't been enough for me, either. I don't know much about graph theory.

In particular, I don't know why adding the terms of a graph-related sequence would be of significance.

Viliam Furik · 2020-11-01, 22:37

First of all, I admit the number is not as special as other numbers I could have chosen.

3,560,600,696,674 - number of tree graphs with at most 35 vertices.

The specialness of this number lies in the Graceful Tree Conjecture, which states that all trees are graceful (there exists at least one graceful labelling for every tree graph). It has been verified by computers for all trees with at most 35 vertices. So far, every tree checked has at least one graceful labelling.

This conjecture is of particular interest to me because I am trying to prove it, together with my schoolmate, but also because 6 mathematicians that have participated in its research were from Slovakia, namely Anton Kotzig and Alexander Rosa (these two, together with Gerhard Ringel, are the ones that conjectured it), Alfonz Haviar and Pavel Hrnčiar (published a result that every tree with a diameter at most 5 is graceful), and Miroslav Haviar and Michal Ivaška.

-------
EDIT: I give up my turn to choose a new number.

Dr Sardonicus · 2020-11-02, 00:44

Quote:

Originally Posted by Viliam Furik

3,560,600,696,674 - number of tree graphs with at most 35 vertices.

The specialness of this number lies in the Graceful Tree Conjecture, which states that all trees are graceful (there exists at least one graceful labelling for every tree graph). It has been verified by computers for all trees with at most 35 vertices. So far, every tree checked has at least one graceful labelling.

(Google Google) Huh. "Number of trees with n vertices" turns up formula n^n-2. Wait, those numbers are WAY too big. (Scribble scribble) Oh, that's if the vertices are labeled. Not what we want.

We want the number of "different" trees with n vertices. OK, got it. OEIS A000055. Number of trees with n unlabeled nodes.

Enough terms to verify the total are given at A000055 as a simple table.

swishzzz · 2020-11-13, 04:50

66600049

LaurV · 2020-11-13, 09:02

Not fun, it is the first link gugu gives.

(however, we learned a couple of things from it! thanks for sharing, but the search was indeed not fun haha, too easy)

2020-11-01, 22:37	#445
Viliam Furik "Viliam Furík" Jul 2018 Martin, Slovakia 3²·43 Posts	First of all, I admit the number is not as special as other numbers I could have chosen. 3,560,600,696,674 - number of tree graphs with at most 35 vertices. The specialness of this number lies in the Graceful Tree Conjecture, which states that all trees are graceful (there exists at least one graceful labelling for every tree graph). It has been verified by computers for all trees with at most 35 vertices. So far, every tree checked has at least one graceful labelling. This conjecture is of particular interest to me because I am trying to prove it, together with my schoolmate, but also because 6 mathematicians that have participated in its research were from Slovakia, namely Anton Kotzig and Alexander Rosa (these two, together with Gerhard Ringel, are the ones that conjectured it), Alfonz Haviar and Pavel Hrnčiar (published a result that every tree with a diameter at most 5 is graceful), and Miroslav Haviar and Michal Ivaška. ------- EDIT: I give up my turn to choose a new number. Last fiddled with by Viliam Furik on 2020-11-01 at 22:45

2020-11-13, 09:02	#448
LaurV Romulan Interpreter Jun 2011 Thailand 5²×7×53 Posts	Not fun, it is the first link gugu gives. (however, we learned a couple of things from it! thanks for sharing, but the search was indeed not fun haha, too easy) Last fiddled with by LaurV on 2020-11-13 at 09:03

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2020-11-01, 10:37	#443
mart_r Dec 2008 you know...around... 2·313 Posts	Hmm... I wanted to post a new number, but still can't figure out Viliam Furik's number. And I don't know much about graph theory either.

2020-11-01, 21:46	#444
Dr Sardonicus Feb 2017 Nowhere 2²·5·7·31 Posts	I'm afraid the hints haven't been enough for me, either. I don't know much about graph theory. In particular, I don't know why adding the terms of a graph-related sequence would be of significance.

2020-11-13, 04:50	#447
swishzzz Jan 2012 Toronto, Canada 2×3³ Posts	66600049