Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying with a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.
Let be a quasigroup. Associativity of the operation on can be expressed by the symbolic identity of left and right multiplication maps; likewise, commutativity can be expressed by the identity . In this article, we investigate symmetric linear identities: these are identities in left and right multiplication symbols in which every indeterminate appears exactly once on each side, and whose sides are mirror images of each other. We determine precisely which identities imply associativity and...
The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.
The goal of this paper is at least two-fold. First we attempt to give a survey of some recent (and developed up to the time of the Banach Center workshop Parameter Spaces, February '94) applications of the theory of symmetric polynomials and divided differences to intersection theory. Secondly, taking this opportunity, we complement the story by either presenting some new proofs of older results (and this takes place usually in the Appendices to the present paper) or providing some new results which...
We characterize which automorphisms of an arbitrary complete bipartite graph can be induced by a homeomorphism of some embedding of the graph in S³.
In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.
The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.
We examine iteration graphs of the squaring function on the rings when , for a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when and when and are symmetric when .