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Jan
31
comment Recurrence equation similar to a geometric progression
@leonbloy no, I meant the initial conditions ($T(1) = A$ and $T(n) = B$).
Nov
30
comment Distribution probability of elements and pair-wise differences in a sorted list
Indeed, thanks for this great answer :-)
Nov
30
awarded  Supporter
Nov
30
comment Distribution probability of elements and pair-wise differences in a sorted list
Thanks for the answer! I actually had that after I posted the question, but I was not able to check that $\sum_{i=0}^{N-1} \Pr(x_i = x) = 1$, and somehow started doubting on it. The way you put it makes sense though, and I did that sum numerically which seems to be right! A note on $d$: it seems that $\Pr(d_i = 0) = \frac m {N-m+1} > 0$ which makes no sense if elements are unique... Yet you did take that into account in the pdf of $x_i$. Any idea ?
Nov
29
revised Distribution probability of elements and pair-wise differences in a sorted list
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Nov
28
revised Distribution probability of elements and pair-wise differences in a sorted list
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Nov
28
asked Distribution probability of elements and pair-wise differences in a sorted list
Oct
19
revised Recurrence equation similar to a geometric progression
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Oct
19
revised Evaluating a recurrence relation with non-contiguous initial conditions
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revised Evaluating a recurrence relation with non-contiguous initial conditions
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revised Evaluating a recurrence relation with non-contiguous initial conditions
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Oct
10
revised Recurrence equation similar to a geometric progression
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revised Evaluating a recurrence relation with non-contiguous initial conditions
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Oct
9
revised Recurrence equation similar to a geometric progression
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revised Evaluating a recurrence relation with non-contiguous initial conditions
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revised Recurrence equation similar to a geometric progression
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revised Evaluating a recurrence relation with non-contiguous initial conditions
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Sep
19
comment Evaluating a recurrence relation with non-contiguous initial conditions
Thank you for your answer. However, I am not looking for solving the recurrence, but rather evaluating the $T(i)$.
Sep
19
asked Evaluating a recurrence relation with non-contiguous initial conditions
Sep
17
revised Recurrence equation similar to a geometric progression
Reformulate the question, there does not seem to be a closed form solution