منابع مشابه
Whitney Number Inequalities for Geometric Lattices
Let L be a finite geometric lattice of rank r, and for i =0, I, •• •» r, let W. denote the number of elements of L with rank i. F or 1 < k < r 2, we have W, + W. + • • • + V, < W ,+•••+ W ., + W , 12 fe r—k r—l r—1 with equality if and only if the lattice L is modular. We give two further results concerning matchings of lattice elements of rank < k into those of rank > r — k, and observe that a...
متن کاملSome results on Whitney numbers of Dowling lattices
In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is a relation between Stirling and Eulerian polynomials. Can we find a new relation between Dowling polynomials and other polynomials generalizing Eulerian polynomials? In addition, some congruences for the Dowling numbers are given. Mathematics Subject...
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 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 کاملTranslated 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.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1975
ISSN: 0001-8708
DOI: 10.1016/0001-8708(75)90145-0