Two pages of a note on the Newton's interpolation series (and
related topics) when generalized to the functions of more
variables. The text is in fact an extended abstract by itself (I
have its Russian version but it is told to have been translated).
Compact - even at a cost that there is virtually no blank space so
that the compression is terrific: 14 references on 11 lines etc.
Numerous abbreviations (typically: h.B.o. B(m,n) for the higher
Bruhat orders, with definition to be sought in ref. [1]).
Difficult to read, also due to this maximal economy in notation.
The core of the message is Theorem 1 which relates the highest
coefficients in all the concepts listed in the title. After some
decoding  (all - and there are quite a few of them - equations
are set just in the running-text format) you find this quintuple
interrelation quite interesting.


MR2152956 Il\cprime yuta, G. G. Sylvester sub-resultants, 
rational Cauchy approximations, Thiele's continued fractions, and 
higher Bruhat orders. (Russian) Uspekhi Mat. Nauk 60 (2005), no. 
2(362), 165--166; translation in Russian Math. Surveys 60 (2005), 
no. 2, 354--356