New combinatorial interpretations ofr-Whitney andr-Whitney–Lah numbers
نویسندگان
چکیده
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 کاملCombinatorial Interpretations for the Markov Numbers
We need to put in an abstract, but we can do this last. 1 Markov Polynomials We define Markov polynomials to be triples of polynomials (f(x,y,z), g(x,y,z), h(x,y,z)) that satisfy the relation f 2 + g + h = x + y + z xyz fgh Equivalently, we may rewrite this as f 2 + g + h fgh = K(x, y, z), K(x, y, z) := x + y + z xyz Clearly the triple (x,y,z) satisfies this relation. To generate another Markov...
متن کاملCombinatorial Interpretations for the Markoff Numbers
In this paper we generalize the concept of Markoff numbers with the construction of Markoff polynomials. We then present a combinatorial model based on a family of recursively-defined graphs which we call snakes, such that the Markoff polynomials and Markoff numbers are respectively weighted and unweighted enumerators of the perfect matchings of snakes. We have found four proofs of the central ...
متن کاملCombinatorial Interpretations of the Jacobi-Stirling Numbers
The Jacobi-Stirling numbers of the first and second kinds were introduced in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers. Andrews and Littlejohn have recently given a combinatorial interpretation for the second kind of the latter numbers. Noticing that these numbers are very similar to the classical central factorial numbers, we give combinatorial interpr...
متن کاملPrefab posets' Whitney numbers
We introduce a natural partial order ≤ in structurally natural finite subsets the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers' triangular array-are then calculated and the explicit formula for them is provided. Next-in the second construction-we endow the set sums of prefa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.08.020