Searcharxiv⌕ Search

arXiv subjects

Leonid Bedratyuk

Publications and source records attributed to Leonid Bedratyuk.

At least 37 records · Page 2Linked to original sources
arXiv2012

Derivations and identities for Kravchuk polynomials

We introduce the notion of Kravchuk derivations of the polynomial algebra. We prove that any element of the kernel of the derivation gives a polynomial identity satisfied by the Kravchuk polynomials. Also, we prove that any kernel element of the basic Weitzenbök derivations yields a polynomial identity satisfied by the Kravchuk polynomials. We describe the corresponding intertwining maps.

math.CO↗
arXiv2012

Derivations and identities for Fibonacci and Lucas polynomials

We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any polynomial identity for Appel polynomial yields a polynomial identity for the Fibonacci and Lucas polynomials and describe the corresponding intertwining maps.

math.RA↗
arXiv2011

Multivariate Poincaré series for algebras of $SL_2$-invariants

Let $\mathcal{C}_{\mathbi{d}},$ $\mathcal{I}_{\mathbi{d}},$ $\mathbi{d}{=}(d_1,d_2,..., d_n)$ be the algebras of join covariants and joint invariants of the $n$ binary forms of degrees $d_1,d_2,..., d_n.$ Formulas for computation of the multivariate Poincaré series $\mathcal{P}(\mathcal{C}_{\mathbi{d}},z_1,z_2,...,z_n,t)$ and $\mathcal{P}(\mathcal{I}_{\mathbi{d}},z_1,z_2,...,z_n)$ are found.

math.AG↗
arXiv2011

The MAPLE package for calculating Poincaré series

We offer a Maple package {\tt Poincare\_Series} for calculating the Poincaré series for the algebras of invariants/covariants of binary forms, for the algebras of joint invariants/covariants of several binary forms, for the kernel of Weitzenböck derivations and for the multivariate Poincaré series of algebras of joint invariants/covariants of several binary forms.

math.AG↗