- #1
LuHell
- 1
- 0
Hi,
I am reading a paper and I am trying to understand an equality which is given without proof:
[tex]\sum_{k=1}^s\binom{2s-k}{s}\frac{k}{2s-k}v^k(v-1)^{s-k}=v\sum_{k=0}^{s-1}\binom{2s}{k}\frac{s-k}{s}(v-1)^{k} [/tex]
Here, s>0, k and v are positive integers.
The equality in question appears in Lemma 2.1 of
http://web.williams.edu/Mathematics.../graphs/mckay_EigenvalueLargeRandomGraphs.pdf
Would you be kind and give me some insights on how to derive this equality?
Thank you,
LH
I am reading a paper and I am trying to understand an equality which is given without proof:
[tex]\sum_{k=1}^s\binom{2s-k}{s}\frac{k}{2s-k}v^k(v-1)^{s-k}=v\sum_{k=0}^{s-1}\binom{2s}{k}\frac{s-k}{s}(v-1)^{k} [/tex]
Here, s>0, k and v are positive integers.
The equality in question appears in Lemma 2.1 of
http://web.williams.edu/Mathematics.../graphs/mckay_EigenvalueLargeRandomGraphs.pdf
Would you be kind and give me some insights on how to derive this equality?
Thank you,
LH