منابع مشابه
Translated Whitney and r-Whitney Numbers: A Combinatorial Approach
Using a combinatorial approach, we introduce the translated Whitney numbers. This seems to be more natural than to write a product of anarithmetical progression in terms of a power variable and conversely. We also extend our ideas to translated r-Whitney numbers of both kinds and to translated Whitney-Lah numbers.
متن کاملA note on the r-Whitney numbers of Dowling lattices
The complete and elementary symmetric functions are specializations of Schur functions. In this paper, we use this fact to give two identities for the complete and elementary symmetric functions. This result can be used to proving and discovering some algebraic identities involving rWhitney and other special numbers.
متن کاملSome Theorems and Applications of the (q, r)-Whitney Numbers
The (q, r)-Whitney numbers were recently defined in terms of the q-Boson operators, and several combinatorial properties which appear to be q-analogues of similar properties were studied. In this paper, we obtain elementary and complete symmetric polynomial forms for the (q, r)-Whitney numbers, and give combinatorial interpretations in the context of A-tableaux. We also obtain convolution-type ...
متن کاملWillmore Surfaces of R 4 and the Whitney Sphere ?
We make a contribution to the study of Willmore surfaces in four-dimensional Euclidean space R4 by making use of the identification of R4 with two-dimensional complex Euclidean space C2. We prove that the Whitney sphere is the only Willmore Lagrangian surface of genus zero in R4 and establish some existence and uniqueness results about Willmore Lagrangian tori in R4 ≡ C2. Mathematics Subject Cl...
متن کاملOn q-Boson Operators and q-Analogues of the r-Whitney and r-Dowling Numbers
We define the (q, r)-Whitney numbers of the first and second kinds in terms of the q-Boson operators, and obtain several fundamental properties such as recurrence formulas, orthogonality and inverse relations, and other interesting identities. As a special case, we obtain a q-analogue of the r-Stirling numbers of the first and second kinds. Finally, we define the (q, r)-Dowling polynomials in t...
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ژورنال
عنوان ژورنال: Journal of Industrial & Engineering Chemistry
سال: 1921
ISSN: 0095-9014,1943-2968
DOI: 10.1021/ie50134a020