This paper shows the universal representations of symmetric functions with multidimensional variable-size variables, which help assessing the justification of approximation methods aggregating the information of each variable by moments. It then discusses how the results give insights into economic...
This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, e...
Descents in permutations or words are defined from the relative position of two consecutive letters. We investigate a statistic involving patterns of k consecutive letters, and show that it leads to Hopf algebras generalizing noncommutative symmetric functions and quasi-symmetric functions.
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative...
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of a factorization for compositions: equivalent compositions ha...
Un nouveau plan pour l'Algèbre, chapitre V (corps commutatifs) est proposé. Il est composé de 9 paragraphes et de deux appendices. Le contenu des paragraphes est discuté en détail. Le premier appendice sur les fonctions symétriques est jugé insuffisant en l'état. La lecture de l'appendice II, sur le...