Related papers: Generalized Chacon polynomial constructions
We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a…
In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the…
We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of…
We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies…
We prove that the super-linearizability of polynomial systems is preserved by all currently known classes of polynomial automorphisms of $\R^n$. We then establish connections between such automorphisms and a sufficient condition for…
The present work is devoted to the extension of some general properties of automorphisms and derivations which are known for Lie algebras to finite dimensional complex Leibniz algebras. The analogues of the Jordan-Chevalley decomposition…
A CR version of the Greene-Krantz theorem \cite{GK} for the semicontinuity of complex automorphism groups will be provided. This is not only a generalization but also an intrinsic interpretation of the Greene-Krantz theorem.
In this paper we prove that over algebraically closed field $K$ of positive characteristic $\neq 2$ every automorphism of the group of origin-preserving automorphisms of the polynomial algebra $K[x_1,\ldots, x_n]$ ($n>3$) which fixes every…
We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements…
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…
Classical binomial identities are established by giving probabilistic interpretations to the summands. The examples include Vandermonde identity and some generalizations.
We provide an elementary and self-contained derivation of formulae for products and ratios of characteristic polynomials from classical groups using classical results due to Weyl and Littlewood.
We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…
The characteristic polynomials of the adjacency matrix of line graphs of caterpillars and then the characteristic polynomials of their Laplacian or signless Laplacian matrices are characterized, using recursive formulas. Furthermore, the…
We present an elementary identity for the cyclotomic polynomials $\Phi_n(X)$ which reflects a kind of multiplicative property of $\Phi_n(X)$ as a function of $n$, and we explore its connections with the properties of other arithmetical…
The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with…
Let ${\cal P}$ be the set of palindromes occurring in the Fibonacci sequence. In this note, we establish three structures of $\mathcal{P}$ and and discuss their properties: cylinder structure, chain structure and recursive structure. Using…
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers,…
We present a list of all polynomial dominanting maps of the complex plane with branched value curve isomorphic to the complex line, up to polynomial automorphisms.
A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based…