Claudia Malvenuto

Stable sets of maximal size in Kneser-type graphs

We introduce a family of vertex-transitive graphs with specified subgroups of automorphisms which generalise Kneser graphs, powers of complete graphs and Cayley graphs of permutations. We compute the stability ratio for a wide class of these. Under certain conditions we characterise their stable sets of maximal size.

Plethysm and conjugation and quasi-symmetric functions

Abstract Let F C denote the basic quasi-symmetric functions, in Gessels notation (1984) ( C any composition). The plethysm s λ oF C is a positive linear combination of functions F D . Under certain conditions, the image under the involution ω of a quasi-symmetric function defined by equalities and inequalities of the variables is obtained by negating the inequalities.

Pairwise colliding permutations and the capacity of infinite graphs

We call two permutations of the first n naturals colliding if they map at least one number to consecutive naturals. We give bounds for the exponential asymptotics of the largest cardinality of any set of pairwise colliding permutations of [n]. We relate this problem to the determination of the Shannon capacity of an infinite graph and initiate the study of analogous problems for infinite graphs with finite chromatic number.

A self paired Hopf algebra on double posets and a Littlewood-Richardson rule

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra. We define a symmetric bilinear form on this Hopf algebra: it counts the number of pictures (in the sense of Zelevinsky) between two double posets. This form is a Hopf pairing, which means that product and coproduct are adjoint each to another. The product and coproduct correspond respectively to disjoint union of posets and to a natural decomposition of a poset into order ideals. Restricting to special double posets (meaning that the second order is total), we obtain a notion equivalent to Stanleys labelled posets, and a Hopf subalgebra already considered by Blessenohl and Schocker. The mapping which maps each double poset onto the sum of the linear extensions of its first order, identified via its second (total) order with permutations, is a Hopf algebra homomorphism, which is isometric and preserves the internal product, onto the Hopf algebra of permutations, previously considered by the two authors. Finally, the scalar product between any special double poset and double posets naturally associated to integer partitions is described by an extension of the Littlewood-Richardson rule.

Graph-Different Permutations

For a finite graph

Evacuation of labelled graphs

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P-Partitions and the plactic congruence

whose vertices are different natural numbers we call two infinite permutations of the natural numbers

Cyclic colliding permutations

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Some Results on Two Conjectures of Schützenberger

-different if they have two adjacent vertices of

Corrigendum: Corrigendum to “enumerating permutation polynomials---I: Permutations with non-maximal degree”

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