A generalization of the binomial coefficients
โ Scribed by Daniel E. Loeb
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 614 KB
- Volume
- 105
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let ! be a complex variable. We associate a polynomial in !, denoted ( M N ) ! , to any two molecular species M=M(X) and N=N(X) by means of a binomial-type expansion of the form In the special case M(X)=X m , the species of linear orders of length m, the above formula reduces to the classical binom
Generalized binomial coefficients of the first and second kind are defined in terms of object selection with and without repetition from weighted boxes. The combinatorial definition unifies the binomial coefficients, the Gaussian coefficients, and the Stirling numbers and their recurrence relations
Let q be a prime number. The number of subgroups of order qk in an abelian group G of order qn and type 2 is a polynomial in q, [ak']~. In 1987, Lynne Butler showed that the first difference, I-~,'] -[ka-'~], has nonnegative coefficients as a polynomial in q, when 2k ~< 12[. We generalize the first