Some results on Whitney numbers of Dowling lattices
نویسندگان
چکیده
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 Classification: 05B35; 05A15; 11B73
منابع مشابه
A 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 کاملThe Translated Dowling Polynomials and Numbers
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated D...
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...
متن کاملGeometric Lattices of Structured Partitions
*Research and preparation of this report were substantially assisted by National Science Foundation grants DMS-8407102 and DMS-8606102. For certain matroids on the edges of a graph, digraph, or bidirected graph with group gains (edge labels from a group), the ats form intriguing new geometric lattices whose Whitney numbers have geometrical signiicance. In this chapter, the rst of a series, we l...
متن کاملOn Whitney numbers of the order ideals of generalized fences and crowns
We solve some recurrences given by E. Munarini and N. Zagaglia Salvi proving explicit closed formulas for Whitney numbers of the distributive lattices of order ideals of the fence poset and crown poset. Moreover, we get explicit closed formulas for Whitney numbers of lattices of order ideals of fences with higher asymmetric peaks.
متن کامل