3,065 reputation
1822
bio website puremaths.open.ac.uk/People/…
location United Kingdom
age 52
visits member for 3 years, 2 months
seen Jul 18 at 12:31

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.


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 $N=0,1,\ldots,40$.
Jun
14
revised Number of solution for $xy +yz + zx = N$
added tag
Jun
10
revised Interestingly restricted compositions of $n$
added 2 characters in body
Jun
10
comment Interestingly restricted compositions of $n$
Your expression for $A(x)$ seems incorrect; it doesn't expand to the correct series.
Jun
10
answered Interestingly restricted compositions of $n$
Jun
10
revised Bijection between multisets and directed animals?
added 46 characters in body
Jun
10
revised Bijection between multisets and directed animals?
edited body