相关论文: Complementary Algorithms For Tableaux

We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…

In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.

A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…

We introduce a new row insertion algorithm on decreasing tableaux and increasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivial variation of Hecke column insertion which generalizes EG…

We give a new combinatorial interpretation of Howe dual pairs of the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to…

We consider nonsymmetric operads with two binary operations satisfying relations in arity 3; hence these operads are quadratic, and so we can investigate Koszul duality. We first consider operations which are nonassociative (not necessarily…

An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed…

This paper presents a combinatorial study of the super plactic monoid of type A, which is related to the representations of the general linear Lie superalgebra. We introduce the analogue of the Sch\"{u}tzenberger's jeu de taquin on the…

The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the…

A K-theoretic analogue of RSK insertion and Knuth equivalence relations was first introduced in 2006 by Buch, Kresch, Shimozono, Tamvakis, and Yong. The resulting K-Knuth equivalence relations on words and increasing tableaux on [n] has…

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains…

Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…

The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…

We establish a symmetrization procedure in a context of general orthogonal expansions associated with a second order differential operator $L$, a `Laplacian'. Combined with a unified conjugacy scheme furnished in our earlier article it…

The character theory of symmetric groups, and the theory of symmetric functions, both make use of the combinatorics of Young tableaux, such as the Robinson-Schensted algorithm, Schuetzenberger's "jeu de taquin", and evacuation. In 1995…

In this manuscript we show that two partial orders defined on the set of standard Young tableaux of shape $\alpha$ are equivalent. In fact, we give two proofs for the equivalence of the box order and the dominance order for {tableaux}. Both…

We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the…

In two seminal papers M. Kontsevich introduced graph homology as a tool to compute the homology of three infinite dimensional Lie algebras, associated to the three operads `commutative,' `associative' and `Lie.' We generalize his theorem to…

We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…