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Jun
10
comment Hex game winning strategy
It's not clear from the question what the board layout is (you can do ASCII art by putting 4 spaces before each line, and there are online designs for ASCII art hexagons), or what the rules of the game are.
May
21
comment Deterministic Push-Down Automata
Is $U$ a terminal? And as a hint: have you tried building a non-deterministic push-down automaton to recognise this language?
May
21
comment What is one way to prove that there exists no ellipse that matches the exact curvature of the sin wave?
That doesn't rule out the sine wave being less than half of an ellipse.
May
16
comment what is the minimum value of the angles inside these triangles?
I think the question is: what is the smallest angle $\alpha$ such that there exists a dissection of the square into triangles satisfying two properties: that none of the triangles has an internal angle greater than $\alpha$; and that no vertex of a triangle touches another triangle except at a vertex. If so, there's an easy lower bound of 67.5 degrees.
May
6
comment Calculate the Probability for Binary Matrix
I assume that the second sentence means that each element of the matrix is $1$ with probability $p$, but is the third sentence talking about independence of random variables or about linear independence (i.e. the matrix is non-singular)?
Apr
23
comment Repeating cycles in the $3n-1$ problem
Your cycles have a very close link with the cycles of $3n+1$ starting with negative $n$.
Apr
19
comment Return of the lost ant 3D
That such paths exist isn't an problem. Whether or not they have a length is another matter.
Apr
17
comment Maximum number of edges in a (n,n) bipartite graph, that doens't have a complete bipartite subgraph $K_{r,r}$
$c=0$ works for every $r$.
Apr
17
comment Maximum number of edges in a (n,n) bipartite graph, that doens't have a complete bipartite subgraph $K_{r,r}$
There's a trivial solution: let $c=0$. If $r=1$ then that's tight.
Apr
17
comment Prove that there are two frogs in one square.
Harry Dunlop's answer already provides a solution: this is essentially just Hilbert's Hotel backwards.
Apr
15
comment Game Theory - Voting
The procedure as described doesn't seem to always select a winner. If A gets 51%, B gets 49%, C gets 0%, and D gets 0% then the first round of eliminations should ditch C and D, but neither A or B can be eliminated.
Apr
15
comment Proof that 12 in a row tic-tac-toe is a tie game?
Tic-tae-toe on an infinite grid can never end in a tie. Presumably you mean that neither player has a winning strategy.
Apr
11
comment closed form of a specific crazy summation?
It looks like you have a closed form already.
Apr
8
comment Round Robin for Team Matches
Does en.wikipedia.org/wiki/… help?
Apr
8
comment Making 7 vertices triangle free graph bipartite by deleting an edge
There's a trivial counter-example: the graph with $|V|=7$ and $|E|=0$.
Apr
7
comment Characterizing a certain set of matrices arising from binary trees
Your diagram doesn't look like a binary tree. It could be converted into a binary tree by inserting three non-leaf nodes, but if this is done symmetrically then the distances between leaf nodes would be $2$ and $4$. What is the actual tree structure?
Apr
4
comment Josephus Variant
You might want to check your results against oeis.org/A032434.
Apr
2
comment Minimal DFA for a given regular expression
Are you familiar with the Myhill-Nerode theorem?
Mar
29
comment Are there useful combinatorial constructions of grammars?
I don't have enough to make an answer, and you stand more chance of getting a more complete answer if I stick to comments. But Flajolet and Sedgewick's book on Analytic Combinatorics seems to address something related to context-free grammars, so you might want to try to find a copy.
Mar
28
comment Are there useful combinatorial constructions of grammars?
I think you need to be a bit more careful in distinguishing between a rule from a CFG and the CFG itself. I can understand that you might want to identify the CFG with the rule which defines its initial non-terminal, but things might become clearer if you define the size of a rule as the number of symbols in its definition and the size of a grammar as the sum of the sizes of the rules reachable from its initial non-terminal. For a start, that immediately highlights the importance of the transitive closure, and suggests looking at graph combinatorics.