Encontrados 17 documentos, a visualizar página 1 de 2
On noncrossing and nonnesting partitions of type D
Conflitti, Alessandro; Mamede, RicardoWe present an explicit bijection between noncrossing and nonnesting partitions of Coxeter systems of type D which preserves openers, closers and transients. ; Centro de Matemática da Universidade Coimbra; Fundação para a Ciência e a Tecnologia Grant SFRH/BPD/30471/2006.
A bijection between noncrossing and nonnesting partitions of types A, B and C
Mamede, RicardoThe total number of noncrossing partitions of type is the nth Catalan number 1 n+1 2n n when = An−1, and the coefficient binomial 2n n when = Bn or Cn, and these numbers coincide with the correspondent number of nonnesting partitions. For type A, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each crossing to a nesting, is one of them. In ...
On an index two subgroup of puzzle and Littlewood-Richardson tableau Z2 x S3-sy...
Azenhas, Olga; Conflitti, Alessandro; Mamede, RicardoWe consider an action of the dihedral group Z2 × S3 on Littlewood- Richardson tableaux which carries a linear time action of a subgroup of index two. This index two subgroup action on Knutson-Tao-Woodward puzzles is the group generated by the puzzle mirror reflections with label swapping. One shows that, as happens in puzzles, half of the twelve symmetries of Littlewood-Richardson coefficients may also be exhib...
Linear time equivalence of Littlewood-Richardson coefficient symmetry maps
Azenhas, Olga; Conflitti, Alessandro; Mamede, RicardoBenkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the conjugation symmetry of the Littlewood–Richardson coefficients, i.e. c μ, = c t μt, t . Tableau–switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon–Sundaram maps are versions of that bijection. In this paper one exhibits explici...
Labour mobility, industry evolution and social networks: a co-evolutionary model
Mamede, RicardoDINÂMIA, Setembro de 2008. ; This paper presents a model that was built in order to analyse the interdependencies between labour market dynamics and the evolution of industries’ structure, in situations where interpersonal links among workers influence individuals’ job decisions. The model was inspired by the case of industries that rely heavily on highly skilled labour and in which problems of incomplete info...
On (0,1)-matrices with prescribed row and column sum vectors
Fonseca, C. M. da; Mamede, RicardoGiven partitions R and S with the same weight, the Robinson-Schensted- Knuth correspondence establishes a bijection between the class A(R, S) of (0, 1)- matrices with row sum R and column sum S and pairs (P,Q) of Young tableaux of conjugate shapes and , with S 4 4 R. An algorithm for constructing a matrix in A(R, S) whose insertion tableaux has a prescribed shape with S 4 4 R, is provided. We generaliz some...
An algorithm for the inertia sets of tree sign patterns
Fonseca, C. M. da; Mamede, RicardoA matrix whose entries are +, ¡ or 0 is said a sign pattern. The inertia set of an n-by-n symmetric sign pattern A is the set of inertias of all real symmetric matrices with the same sign pattern as A. We present an algorithm to compute the inertia set of any symmetric tree (or acyclic) sign pattern. The procedure generalizes some recent results. Some examples are provided. ; Centro de Matemática da Universi...
Key polynomials, invariant factors and an action of the symmetric group on Youn...
Azenhas, Olga; Mamede, RicardoWe give a combinatorial description of the invariant factors associated with certain sequences of product of matrices, over a local principal ideal domain, under the action of the symmetric group by place permutation. Lascoux and Sch¨utzenberger have defined a permutation on a Young tableau to associate to each Knuth class a right and left key which they have used to give a combinatorial description of a key po...
Keys associated with the symmetric group S4 and matrix realizations of pairs of...
Azenhas, Olga; Mamede, RicardoA variant of the dual RSK correspondence [10, 12] gives a bijection between classes of skew-tableaux and tableau-pairs of conjugate shapes. The problem of a matrix realization, over a local principal ideal domain with prime p, of the pair (T ,K(σ)) with K(σ) a key associated with the permutation σ ∈ St, and T a skew-tableau with the same evaluation as K(σ), is addressed. If T corresponds by this variant of the ...
Action of the symmetric group on sets of skew-tableaux with prescribed matrix r...
Azenhas, Olga; Mamede, RicardoLet M be the set of all rearrangements of t fixed integers in 1, ... , n. We consider those Young tableaux , of weight (m1, ... , mt) in M, arising from a sequence of products of matrices over a local principal ideal domain, with maximal ideal (p),where [Delta]a is an n × n nonsingular diagonal matrix, with invariant partition a, and U is an n × n unimodular matrix. Given a partition a and an n × n unimodular m...
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