Related papers: Equality of multiplicity free skew characters

The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In…

We revive the concept of Lambda-freeness of Mlotkowski, which describes a mixture of classical and free independence between algebras of random variables. In particular, we give a description of this in terms of cumulants; this will be…

A study is carried out of the elementary theory of quotients of symmetric groups in a similar spirit to [Sh:24]. Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S(mu) on an infinite…

Let $k$ be a nonnegative integer, and let $\alpha$ and $\beta$ be two permutations of $n$ symbols. We say that $\alpha$ and $\beta$ $k$-commute if $H(\alpha\beta, \beta\alpha)=k$, where $H$ denotes the Hamming metric between permutations.…

An association scheme is called skew-symmetric if it has no symmetric adjacency relations other than the diagonal one. In this paper, we study 4-class skew-symmetric association schemes. In J. Ma [On the nonexistence of skew-symmetric…

Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…

The notion of graph acyclicity has been extended to several different notions of hypergraph acyclicity, in increasing order of generality: gamma acyclicity, beta acyclicity, and alpha acyclicity, that have met a great interest in many…

We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\alpha_n}, {n-1}^{\alpha_{n-1}},..., 1^{\alpha_1})$, where $\alpha = (\alpha_1,...,\alpha_n)$ is a composition, or the $180^\circ$ rotation of…

For the parabolic obstacle-problem-like equation $$\Delta u - \partial_t u = \lambda_+ \chi_{\{u>0\}} - \lambda_- \chi_{\{u<0\}} ,$$ where $\lambda_+$ and $\lambda_-$ are positive Lipschitz functions, we prove in arbitrary finite dimension…

Let $ \Phi=(G, \varphi) $ be a connected complex unit gain graph ($ \mathbb{T} $-gain graph) on a simple graph $ G $ with $ n $ vertices and maximum vertex degree $ \Delta $. The associated adjacency matrix and degree matrix are denoted by…

In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…

In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…

For $K$ an abstract elementary class with amalgamation and no maximal models, we show that categoricity in a high-enough cardinal implies structural properties such as the uniqueness of limit models and the existence of good frames. This…

Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of…

Let $\mathbb{Q}(\alpha)$ and $\mathbb{Q}(\beta)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $\mathbb{Q}(\beta) \rightarrow \mathbb{Q}(\alpha)$. The algorithm is particularly efficient if…

Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…

This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus…

We find a simple criterion for the equality $Q_\lambda=Q_{\mu/\nu}$ where $Q_\lambda$ and $Q_{\mu/\nu}$ are Schur's Q-functions on infinitely many variables.

It is proved that all 4-edge-colourings of a (sub)cubic graph are Kempe equivalent. This resolves a conjecture of the second author. In fact, it is found that the maximum degree Delta=3 is a threshold for Kempe equivalence of…

We investigate the poset of skew diagrams ordered by adding or forming the union of skew diagrams. We will show that a skew diagram which has at least n convex corners to the upper left and also to the lower right is larger than the skew…