By sheer coincidence I just stumbled upon http://arxiv.org/abs/1105.3689 Can anyone comment on validity of the statements given? Best, jj * Fred lunnon <fred.lunnon@gmail.com> [Jun 27. 2013 07:15]:
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Returning to examples of tri-wedge convention, here is a classic example actually dubbed in some sources the "hockey stick" identity, and given traditionally in the form for 0 <= k <= n {n\choose k} = \sum_{j = 1}^{n-k+1} {n-j\choose k-1} ; when k = 0 , this relies on defining {-1}_C_{-1} = 1 .
But under the bi-wedge convention --- which I am reluctantly coming round to finding increasingly compelling --- the hockey stick has to give way to the "broken hockey stick" (bifurcated, even?) {n\choose k} = \sum_{j = 1}^{n-k+1} {n-j\choose n-j-k+1} ; not nearly so memorable, sadly.
Fred Lunnon
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