Comments for Peter Cameron's Blog
https://cameroncounts.wordpress.com
always busy counting, doubting every figured guess . . .Thu, 08 Jun 2017 20:12:02 +0000hourly1http://wordpress.com/Comment on Impostor Syndrome by Mike
https://cameroncounts.wordpress.com/2017/06/08/impostor-syndrome/#comment-19690
Thu, 08 Jun 2017 20:12:02 +0000http://cameroncounts.wordpress.com/?p=6062#comment-19690I think everyone suffers from either Dunning-Kruger or Impostor syndrome or both. :::grin::::
The question is the percentage of time either is ascendant.as a cognitive distraction. Cathy O’Neill(Mathbabe) has some related comments about math talent and “genius” recently at her website.
]]>Comment on Impostor Syndrome by jbritnell2013
https://cameroncounts.wordpress.com/2017/06/08/impostor-syndrome/#comment-19687
Thu, 08 Jun 2017 16:30:23 +0000http://cameroncounts.wordpress.com/?p=6062#comment-19687I think most of us realise eventually that everyone else is an impostor too.
]]>Comment on The Sylvester design by Peter Cameron
https://cameroncounts.wordpress.com/2017/06/07/the-sylvester-design/#comment-19686
Thu, 08 Jun 2017 14:05:56 +0000http://cameroncounts.wordpress.com/?p=6059#comment-19686Indeed, GAP assures me that there is no transitive subgroup of order 36 in the automorphism group of the Sylvester graph.
]]>Comment on The Sylvester design by Peter Cameron
https://cameroncounts.wordpress.com/2017/06/07/the-sylvester-design/#comment-19685
Thu, 08 Jun 2017 13:48:13 +0000http://cameroncounts.wordpress.com/?p=6059#comment-19685I think the answer is no. This would require a subgroup of order 36 in S_6.2 which acts transitively on the vertices of the Sylvester graph. I tried a few possibilities and couldn’t find one that works. But it shouldn’t be too hard a job, since such a subgroup would lie inside the normaliser of a Sylow 3-subgroup of S_6.2. Maybe I missed something…
]]>Comment on The Sylvester design by Shahrooz Janbaz
https://cameroncounts.wordpress.com/2017/06/07/the-sylvester-design/#comment-19682
Thu, 08 Jun 2017 12:21:26 +0000http://cameroncounts.wordpress.com/?p=6059#comment-19682The design which you constructed it by Sylvester graph can be used in authentication code construction, as an important area of cryptography. Dear Prof. CameronIs, is the Sylvester graph Cayley?
]]>Comment on Impostor Syndrome by Jon Awbrey
https://cameroncounts.wordpress.com/2017/06/08/impostor-syndrome/#comment-19681
Thu, 08 Jun 2017 11:54:07 +0000http://cameroncounts.wordpress.com/?p=6062#comment-19681I think some people just pretend to have impostor syndrome.
]]>Comment on The Sylvester design by Peter Cameron
https://cameroncounts.wordpress.com/2017/06/07/the-sylvester-design/#comment-19678
Thu, 08 Jun 2017 09:28:55 +0000http://cameroncounts.wordpress.com/?p=6059#comment-19678Interesting! Thanks for this.
My first encounter with the Sylvester graph (though I didn’t know then that it was called that, Norman Biggs had probably named it only a little earlier) was in 1972, back in the days when we didn’t have CFSG and so theorems about multiply-transitive groups were still worth proving. I considered a group G with two different 3-transitive permutation representations so that the stabiliser of a point in each set acts in the same way on both sets. I showed that such a group must be either affine over GF(2) or the symmetric group S_6. In the latter case, I built the graph, and extended it to a Moore graph of diameter 2 and valency n+1, (where n is the degree) from which one concludes that n=6.
]]>Comment on The Sylvester design by David Roberson
https://cameroncounts.wordpress.com/2017/06/07/the-sylvester-design/#comment-19672
Wed, 07 Jun 2017 22:12:09 +0000http://cameroncounts.wordpress.com/?p=6059#comment-19672I happened upon the Sylvester graph in my research recently. I was looking at Gallai graphs of strongly regular graphs. The Gallai graph of a graph G has the edges of G as its vertices, two being adjacent if they share a vertex but are not in a triangle together. If G is the categorical (direct) product of K_6 with itself, then the Gallai graph of G has a maximum independent set (meeting the Delsarte bound) whose elements correspond to edges of G that form a copy of the Sylvester graph. Any maximum independent set of the Gallai graph of this G will correspond to a 5-regular spanning subgraph of G whose distance 1 or 2 graph is also a subgraph of G, and the Sylvester graph is the least common occurring such subgraph (720 times out of 12,911,040 total). The most common is a disjoint union of 6-cliques (1,128,960 occurrences, which correspond to the 6-colorings of the complement of G).
]]>Comment on Notes on Counting by Robert Bailey
https://cameroncounts.wordpress.com/2017/05/15/notes-on-counting/#comment-19570
Thu, 01 Jun 2017 17:37:41 +0000http://cameroncounts.wordpress.com/?p=6050#comment-19570(Shameless advertising) I just ordered it from Blackwells, which had a discount plus free UK delivery….
]]>Comment on Mathematical diversity by Peter Cameron
https://cameroncounts.wordpress.com/2017/05/05/mathematical-diversity/#comment-19547
Tue, 30 May 2017 13:24:39 +0000http://cameroncounts.wordpress.com/?p=6035#comment-19547Sasha Borovik quotes a paper by Amalric and Dehaene, “Origins of the brain networks for advanced mathematics in expert mathematicians”, which you can find at http://www.pnas.org/content/113/18/4909.abstract
They say “Our work addresses the long-standing issue of the relationship between mathematics and language. By scanning professional mathematicians, we show that high-level mathematical reasoning rests on a set of brain areas that do not overlap with the classical left-hemisphere regions involved in language processing or verbal semantics. Instead, all domains of mathematics we tested (algebra, analysis, geometry, and topology) recruit a bilateral network, of prefrontal, parietal, and inferior temporal regions, which is also activated when mathematicians or nonmathematicians recognize and manipulate numbers mentally. Our results suggest that high-level mathematical thinking makes minimal use of language areas and instead recruits circuits initially involved in space and number. This result may explain why knowledge of number and space, during early childhood, predicts mathematical achievement.”
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