---------------Gloria Olive's Erroneous Review----------------
DIALOG(R)File 239:MathSci(R)
(c) 1996 American Mathematical Society. All rts. reserv.
 
  03208075  MR 91b#05021
  A very short proof of Dixon's theorem.
  Ekhad, Shalosh B.
  J. Combin. Theory Ser. A
  Journal of Combinatorial Theory. Series A,   1990,   54,  no. 1,  
141--142.  ISSN: 0097-3165   CODEN: JCBTA7
  Language: English
  Document Type: Journal
  Journal Announcement: 9012
  Subfile: MR (Mathematical Reviews)  AMS
  Abstract Length: SHORT (9 lines)
  Dixon's theorem (as stated) provides a symmetric-type series
representation for the multinomial coefficient $(n+b+c;n,b,c)=R(n)$. The
author attempts to give a very short and very elementary proof by means of
the principle of mathematical induction. After introducing some special
symbols, he states ``since the theorem is obviously true for $n=0$, it
would follow by induction once we show that $(n+1)R(n+1)-(n+b+c+1)R(n)
\equiv0$''. But this identity is an immediate consequence of the definition
for $R(n)$, and hence the ``proof'' lacks validity.
  Reviewer: Olive, Gloria (NZ-OTG)
  Review Type: Signed review
  Descriptors: *05A19 -Combinatorics (For finite fields, see 11Txx)-
Classical combinatorial problems-Combinatorial identities ; 05A10 -
Combinatorics (For finite fields, see 11Txx)-Classical combinatorial
problems-Factorials, binomial coefficients, combinatorial functions (See
also 11B65, 33Cxx)
 
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