Very interesting E-Mail message from Yuval Roichman

From yuvalr@macs.biu.ac.il  Fri Mar 10 06:18:27 2000


Shalom Doron,

I greatly enjoyed reading your paper "The combinatorial astrology
of rabbi Abraham ibn Ezra" (especially the 2nd moral) (i also enjoyed 
the historic insights in the introduction to your paper on Denert's
permutation statistic, given to me by Dominique Foata).

It should be noted that the values of ${7 \choose k}$ are calculated
(very briefly and differently) also in the long commentary 
(PERUSH HAAROCH, there is also PERUSH HAKATZAR) to 
Sefer Shmot Ch 33;v. 21. There he uses symmetricity, and notes 
(in our notation) that ${7 \choose 2}={7\choose 5}$ and 
${7\choose 3}={7 \choose 4}$ ("KENEGDAM" BILSHONO).
I think that this is even more exciting than the recursion rule
of SEFER HAOLAM (especially as ibn ezra has no $n\choose k$ for 
$k=0,1$). 

Perush Haaroch liShmot is one of ibn ezra latest writings.  
Katz, Sela and others (which i've seen) discussing the recursion 
rule of SEFER HAOLAM didn't mention the method in PERUSH HAAROCH 
for computing ${7\choose k}, k=4,5$, which is different (and 
'more elegant'). 

Kol Tuv and Shabat Shalom,

Yuval

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