Fdtxjr

In a future war, an old lady is trying to raise a boy but one of the weapons has made everyone deaf

Recruiter wants very extensive technical details about all of my previous work

What exactly is this small puffer fish doing and how did it manage to accomplish such a feat?

Official degrees of earth’s rotation per day

Is there a data structure that only stores hash codes and not the actual objects?

How do anti-virus programs start at Windows boot?

Why do passenger jet manufacturers design their planes with stall prevention systems?

Define, (actually define) the "stability" and "energy" of a compound

Why Choose Less Effective Armour Types?

compactness of a set where am I going wrong

Most cost effective thermostat setting: consistent temperature vs. lowest temperature possible

What are substitutions for coconut in curry?

How can I track script which gives me "command not found" right after the login?

How Could an Airship Be Repaired Mid-Flight

Hacking a Safe Lock after 3 tries

Can I use USB data pins as power source

How to make healing in an exploration game interesting

Do I need to be arrogant to get ahead?

How to use deus ex machina safely?

Gravity magic - How does it work?

Professor being mistaken for a grad student

What did Alexander Pope mean by "Expletives their feeble Aid do join"?

How could a scammer know the apps on my phone / iTunes account?

What should tie a collection of short-stories together?

Combinatorial proof of Hamiltonian paths on the rook graph

Number of duplicate cases in graphs - hamiltonian and nonhamiltonian pathsCan more than one hamiltonian graph have the same set of hamiltonian paths?Hamiltonian paths in cubic graphRook tour on the chess boardMinimum number of Hamiltonian paths in a strongly connected tournament on $n$ nodesProve that the line graph of a Hamiltonian simple graph is Hamiltonian.Hamiltonian paths in a simple graphHamiltonian cycles and paths in a graphHamiltonian paths in graphHamiltonian paths and cycles of rook graph on $ntimes2$ chessboard

1

$begingroup$

We can be sure that number of Hamiltonian paths on the rook graph for any single cell on $ntimes2$ chessboard equals
$$
H(n+1) = sum_k=0^n
binomnk
binomklfloorfrack2rfloor
left(n-lfloorfrack2rfloorright)!
left(n-lfloorfrack+12rfloorright)!$$
Is there a combinatorial proof for it?

graph-theory hamiltonian-path combinatorial-proofs chessboard

share|cite|improve this question

edited Mar 11 at 19:52

gt6989b

34.9k22557

asked Mar 11 at 19:48

user514787user514787

749310

$endgroup$

add a comment | 

1

$begingroup$

We can be sure that number of Hamiltonian paths on the rook graph for any single cell on $ntimes2$ chessboard equals
$$
H(n+1) = sum_k=0^n
binomnk
binomklfloorfrack2rfloor
left(n-lfloorfrack2rfloorright)!
left(n-lfloorfrack+12rfloorright)!$$
Is there a combinatorial proof for it?

graph-theory hamiltonian-path combinatorial-proofs chessboard

share|cite|improve this question

edited Mar 11 at 19:52

gt6989b

34.9k22557

asked Mar 11 at 19:48

user514787user514787

749310

$endgroup$

add a comment | 

$begingroup$

We can be sure that number of Hamiltonian paths on the rook graph for any single cell on $ntimes2$ chessboard equals
$$
H(n+1) = sum_k=0^n
binomnk
binomklfloorfrack2rfloor
left(n-lfloorfrack2rfloorright)!
left(n-lfloorfrack+12rfloorright)!$$
Is there a combinatorial proof for it?

graph-theory hamiltonian-path combinatorial-proofs chessboard

share|cite|improve this question

edited Mar 11 at 19:52

gt6989b

34.9k22557

asked Mar 11 at 19:48

user514787user514787

749310

$endgroup$

share|cite|improve this question

edited Mar 11 at 19:52

gt6989b

34.9k22557

asked Mar 11 at 19:48

user514787user514787

749310

share|cite|improve this question

edited Mar 11 at 19:52

gt6989b

34.9k22557

asked Mar 11 at 19:48

user514787user514787

749310

edited Mar 11 at 19:52

gt6989b

34.9k22557

edited Mar 11 at 19:52

gt6989b

34.9k22557

asked Mar 11 at 19:48

user514787user514787

749310

asked Mar 11 at 19:48

user514787user514787

749310