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Prove combinatorial inequality

1

0

$begingroup$

I want to know when the following statement is true

$$
f(i)=binomN-i+1i leq binomN-(k-i)+1k-i = g(i),
$$
where $0 leq i leq k$ and $0 leq k leq N$ and $N, k$ are chosen beforehand and $i $ varies.

I've got the following idea, when $i = k/2$ we clearly have equality. We have a symmetry of the equations that $f(k/2 - i) = g(k/2 + i)$. From plotting in Mathematica I get the idea that for $i leq k/2$ the inequality is indeed true, but proving it seems quite difficult.

Are there any Binomial identities one can use for this?

inequality binomial-coefficients

share|cite|improve this question

asked Mar 28 at 0:39

user1792605user1792605

606

$endgroup$

add a comment | 

1

0

$begingroup$

I want to know when the following statement is true

$$
f(i)=binomN-i+1i leq binomN-(k-i)+1k-i = g(i),
$$
where $0 leq i leq k$ and $0 leq k leq N$ and $N, k$ are chosen beforehand and $i $ varies.

I've got the following idea, when $i = k/2$ we clearly have equality. We have a symmetry of the equations that $f(k/2 - i) = g(k/2 + i)$. From plotting in Mathematica I get the idea that for $i leq k/2$ the inequality is indeed true, but proving it seems quite difficult.

Are there any Binomial identities one can use for this?

inequality binomial-coefficients

share|cite|improve this question

asked Mar 28 at 0:39

user1792605user1792605

606

$endgroup$

add a comment | 

$begingroup$

I want to know when the following statement is true

$$
f(i)=binomN-i+1i leq binomN-(k-i)+1k-i = g(i),
$$
where $0 leq i leq k$ and $0 leq k leq N$ and $N, k$ are chosen beforehand and $i $ varies.

I've got the following idea, when $i = k/2$ we clearly have equality. We have a symmetry of the equations that $f(k/2 - i) = g(k/2 + i)$. From plotting in Mathematica I get the idea that for $i leq k/2$ the inequality is indeed true, but proving it seems quite difficult.

Are there any Binomial identities one can use for this?

inequality binomial-coefficients

share|cite|improve this question

asked Mar 28 at 0:39

user1792605user1792605

606

$endgroup$

share|cite|improve this question

asked Mar 28 at 0:39

user1792605user1792605

606

share|cite|improve this question

asked Mar 28 at 0:39

user1792605user1792605

606

asked Mar 28 at 0:39

user1792605user1792605

606

asked Mar 28 at 0:39

user1792605user1792605

606