Beginning with the negative binomial coefficients
, we again find that greater cultural distance and existing immigrant stocks have negative and positive effects, respectively, on the level of the predicted immigrant stock.
3, we know that the total number of these structures is the central binomial coefficient
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
n] (I) is indeed an extension of the usual notion of the binomial coefficient
2 Classical binomial coefficients
of words, shuffle and infiltration
2 where we require a triple alternating sum of products of binomial coefficients
to get an expression for the number of words of [[2k].
Just as with ordinary binomial coefficients
, q-binomial coefficients
have multiple combinatorial interpretations and satisfy many identities, a few of which are highlighted below.
denote the usual q-analogs of numbers, factorials and binomial coefficients
This paper makes use of the recently introduced technique of [gamma]-operators to evaluate the Hankel determinant with binomial coefficient
An application of trinomial revision to the binomial coefficient
ratios in Theorem 3.
The terms [alpha] and [beta] are typical expressions to which 'Rice's method' can be applied, due to the presence of the binomial coefficient
inside an alternating sum.
We use the generalized binomial coefficients
[mathematical expression not reproducible] given by [mathematical expression not reproducible] for n [member of] Z with the convention that [mathematical expression not reproducible] for all integers i < 0.
Topics encompass counting and proofs, sets and logic, graphs and functions, induction, algorithms with ciphers, binomial coefficients
and Pascal's triangle, counting techniques, recurrences, counting and geometry, trees, Euler's formula and applications, graph traversals, graph coloring, probability and expectation, and cardinality.
A note on balancing binomial coefficients
Shane CHERN Communicated by Masaki KASHIWARA, M.
Although the new DGF expression has a very compact form, it involves binomial coefficients
that may cause long runtimes and accuracy problems for large values of upper indices.
The first is the right-circulant determinant sequence with binomial coefficients
and the second is the left-circulant determinant sequence with binomial coefficients