Ribbons and Homogeneous Symmetric Functions

Acyclic Complexes Related to Noncommutative Symmetric Functions

In this paper, we show how to endow the algebra of noncommutative symmetric functions with a natural structure of cochain complex which strongly relies on the combinatorics of ribbons, and we prove that the corresponding complexes are acyclic.

On the conjecture about the nonexistence of rotation symmetric bent functions

In this paper, we describe a different approach to the proof of the nonexistence of homogeneous rotation symmetric bent functions. As a result, we obtain some new results which support the conjecture made in this journal, i.e., there are no homogeneous rotation symmetric bent functions of degree > 2. Also we characterize homogeneous degree 2 rotation symmetric bent functions by using GCD of pol...

Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions

Let hλ, eλ, and mλ denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition λ respectively. We give combinatorial interpretations for the coefficients that arise in expanding mλ in terms of homogeneous symmetric functions and the elementary symmetric functions. Such coefficients are interpreted in terms of cer...

Starlike Functions of order α With Respect To 2(j,k)-Symmetric Conjugate Points

In this paper, we introduced and investigated starlike and convex functions of order α with respect to 2(j,k)-symmetric conjugate points and coefficient inequality for function belonging to these classes are provided . Also we obtain some convolution condition for functions belonging to this class.

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points