1,720,962 research outputs found
The fine structure of 4321 avoiding involutions and 321 avoiding involutions
No full textWe study the fine structure of the sets I(4321) and I(321) connecting the point of wiew of the substitution decomposition theorems with the one of the associated Motzkin paths. The algebraic generating functions of the simple involutions in I(4321) and I(321) are given, together with other generating functions. The simple involutions in I(4321) and I(321) are characterized through their associated Motzkin paths
A geometric interpretation of an equality by Sylvester
No full textAbstractIn this paper, we will show that a classical theorem of topology is, in fact, a combinatorial one, holding in all projective spaces. In the finite case, that is in the case of Galois geometries, this result enables us to obtain many equations between parameters. The easier ones, relating to the complete cell decomposition of Grassmann varieties, are the classical identities introduced by Sylvester in the study of the theory of the partitions. So we start by recalling the Sylvester equality; in Section 2 we shall define Schubert cells and related theorems in the abstract case; finally, in Section 3 we shall consider Galois projective spaces
Remarks on the Variety of Exterior Differential Systems with Homogeneous Polynomials as coefficients
No full textRemarks on the variety of exterior differential system with homogeneous polynomials as coefficients
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Double Graphs
No full textIn this paper we study the elementary properties of double graphs, i.e. of graphs which are the direct product of a simple graph G with the graph obtained by the complete graph K_2 adding a loop to each vertex
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