相关论文: Symmetric Boolean Algebras
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by…
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
We recently introduced the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. There is a type of idempotent system, said to be symmetric. In the present paper we classify up…
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
The symmetric Macdonald polynomials are able to be constructed out of the non-symmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their non-symmetric…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
We introduce a q-analogue MW_q for the meromorphic Weyl algebra, and study the normalization problem and the symmetric powers sym^n(MW_q) for such algebra from a combinatorial viewpoint.
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the…
We investigate sigma-entangled linear orders and narrowness of Boolean algebras. We show existence of sigma-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the…
We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.
In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and…
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding…
Ordinary algebra of formal power series in one variable is convenient to study by means of the algebra of Riordan matrices and the Riordan group. In this paper we consider algebra of formal power series without constant term, isomorphic to…
We bound the tensor ranks of elementary symmetric polynomials, and we give explicit decompositions into powers of linear forms. The bound is attained when the degree is odd.
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…