We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in one-to-one correspondence with outside decompositions for a given skew shape. Outside decompositions are introduced by Hamel and Goulden and are used to give an identity for the skew Schur function that unifies the determinantal expressions for the skew Schur functions i...

Abstract We show that after forcing with a countable support iteration or finite product of Sacks splitting over L , every analytic hypergraph on Polish space admits $\mathbf {\Delta }^1_2$ maximal independent set. This extends an earlier result by Schrittesser (see [25]). As main application we get the consistency $\mathfrak {r} = \mathfrak {u} {i} \omega _2$ together existence $\Delta ^1_2$ u...

Symplectic and orthogonal Schur functions can be defined combinatorially in a manner similar to the classical Schur functions. This paper demonstrates that they can also be expressed as determinants. These determinants are generated using planar decompositions of tableaux into strips and the equivalence of these determinants to symplectic or orthogonal Schur functions is established by Gessel-V...

We use statistical mechanics – variants of the six-vertex model in the plane studied by means of the Yang-Baxter equation – to give new deformations of Weyl’s character formula for classical groups of Cartan type B,C, and D, and a character formula of Proctor for type BC. In each case, the corresponding Boltzmann weights are associated to the free fermion point of the six-vertex model. These de...

Auteur Leruez, Stéphanie [1], Milea, Dan [2], Defoort-Dhellemmes, Sabine [3], Colin, E. [4], Crochet, M. [5], Procaccio, Vincent [6], Ferré, Marc [7], Lamblin, J. [8], Drouin-Garraud, V. [9], Vincent-Delorme, C. [10], Lenaers, Guy [11], Hamel, Christian [12], Blanchet, Catherine [13], Juul, G. [14], Larsen, M. [15], Verny, Christophe [16], Reynier, Pascal [17], Amati-Bonneau, Patrizia [18], Bon...

This paper discusses Hamel’s formalism and its applications to structure-preserving integration of the ndimensional spherical pendulum. It utilizes redundant coordinates in order to eliminate multiple charts on the configuration space of the pendulum as well as nonphysical artificial singularities induced by local coordinates, while keeping the minimal possible degree of redundancy and avoiding...

The value of knowledge assets in creating competitive advantage and subsequently wealth through innovation has never been greater (Teece, 1998). It is increasingly being acknowledged that the resources and the competencies developed within the organisation as well as the mechanisms for building up and reconfiguring these competencies is the only defence against a fierce competition (Penrose, 19...