3,110 reputation
1823
bio website puremaths.open.ac.uk/People/…
location United Kingdom
age 53
visits member for 3 years, 5 months
seen Oct 20 at 13:06

I am studying for a PhD in combinatorics. My research is focussed on enumerative and structural aspects of permutation classes, especially of grid classes.

Previously, I was a software developer, studying combinatorics in my spare time.


Oct
20
comment A counting problem on the integer lattice
@Shibi, I'd misread the question. I've now corrected my answer. It's not just 4-fold symmetry you have to worry about. For example, $(1,7)$ and $(5,5)$ are at the same distance from the origin.
Oct
20
revised A counting problem on the integer lattice
corrected due to misunderstanding of question
Sep
30
awarded  Explainer
Sep
29
answered A counting problem on the integer lattice
Sep
29
comment Countable or uncountable set 8 signs
I stand corrected.
Sep
29
comment Sequence of numbers with prime factorization $pq^2$
@Nishant, the only numbers of the form $pq^2$ having $6$ as a factor are $12$ and $18$.
Jul
2
awarded  Curious
Jun
30
awarded  Yearling
Oct
21
comment How many fours are needed to represent numbers up to $N$?
103 = 44 / .4. + 4
Sep
23
answered Would this be bounded
Jul
25
comment Generating Function for edge-rooted labelled trees
Yes, of course; the labels induce an orientation (of every edge). You didn't state that you were considering labelled trees, but you did state that $T_v(z)$ was the exponential generating function, so that should have been evident.
Jul
25
comment Generating Function for edge-rooted labelled trees
We've both assumed that the edge-root is oriented (i.e. the two ends are distinguishable). If it isn't, then we need to discard one of each asymmetric pair, which gives $T_e(z)=\frac{1}{2}(T_v(z)^2+T_v(z^2))$.
Jul
25
comment Generating Function for edge-rooted labelled trees
This doesn't look correct; you can add a forest of trees to each end of the designated edge (since the two new vertices are external to what is added). It's probably simpler just to take two vertex-rooted trees and identify the roots as the ends of the designated edge, giving $T_e(z)=T_v(z)^2$.
Jun
30
awarded  Yearling
Jun
14
revised What is the smallest alphanumeric string that has 10 million permutations?
edited tags
Jun
14
revised What is the smallest alphanumeric string that has 10 million permutations?
added 241 characters in body
Jun
14
revised What is the smallest alphanumeric string that has 10 million permutations?
added 241 characters in body
Jun
14
answered What is the smallest alphanumeric string that has 10 million permutations?
Jun
14
answered Find the generating function for this set of strings
Jun
14
comment Number of solution for $xy +yz + zx = N$
This seems like a very interesting (and possibly very hard) question. The sequence begins $1, 3, 6, 7, 9, 9, 12, 9, 15, 12, 12, 15, 19, 9, 18, 18, 18, 15, 18, 15, 27, 18, 12, 21, 30, 12, 24, 22, 21, 21, 24, 21, 30, 18, 18, 30, 36, 9, 24, 30, 30$ for $N=0,1,\ldots,40$.