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Ewa Krot-Sieniawska

Publications and source records attributed to Ewa Krot-Sieniawska.

7 recordsLinked to original sources
arXiv2008

On inversion formulas and Fibonomial coefficients

A research problem for undergraduates and graduates is being posed as a cap for the prior antecedent regular discrete mathematics exercises. [Here cap is not necessarily CAP=Competitive Access Provider, though nevertheless ...] The object of the cap problem of final interest i.e. array of fibonomial coefficients and the issue of its combinatorial meaning is to be found in A.K.Kwaśniewski's source papers. The cap problem number seven - still opened for students has been placed on Mathemagics page of the first author [http://ii.uwb.edu.pl/akk/dydaktyka/dyskr/dyskretna.htm]. The indicatory references are to point at a part of the vast domain of the foundations of computer science in ArXiv affiliation noted as CO.cs.DM. The presentation has been verified in a tutor system of communication with a couple of intelligent students. The result is top secret.Temporarily. [Contact: Wikipedia; Theory of cognitive development].

math.CO↗
arXiv2008

On incidence algebras description of cobweb posets

The explicite formulas for Mobius function and some other important elements of the incidence algebra of an arbitrary cobweb poset are delivered. For that to do one uses Kwasniewski's construction of his cobweb posets . The digraph representation of these cobweb posets constitutes a newly discovered class of orderable DAG's named here down KoDAGs with a kind of universality now being investigated. Namely cobweb posets' and thus KoDAGs's defining di-bicliques are links of any complete relations' chains.

math.CO↗
arXiv2008

Characterization of Cobweb Posets as KoDAGs

The characterization of the large family of cobweb posets as DAGs and oDAGs is given. The dim 2 poset such that its Hasse diagram coincide with digraf of arbitrary cobweb poset is constructed.

math.CO↗
arXiv2008

On Characteristic Polynomials of the Family of Cobweb Posets

This note is a response to one of problems posed by A.K. Kwasniewski in one of his recent papers. Namely for the sequence of finite cobweb subposets, the looked for explicit formulas for corresponding sequence of characteristic polynomials are discovered and delivered here. The recurrence relation defining arbitrary family of charactristic polynomials of finite cobweb posets is also derived.

math.CO↗
arXiv2007

An example of algebraization of analysis and Fibonacci cobweb poset characterization

In recent Kwasniewski's papers inspired by O. V. Viskov it was shown that the $ψ$-calculus in parts appears to be almost automatic, natural extension of classical operator calculus of Rota - Mullin or equivalently - of umbral calculus of Roman and Rota. At the same time this calculus is an example of the algebraization of the analysis - here restricted to the algebra of polynomials. The first part of the article is the review of the recent author's contribution. The main definitions and theorems of Finite Fibonomial Operator Calculus which is a special case of $ψ$-extented Rota's finite operator calculus are presented there. In the second part the characterization of Fibonacci Cobweb poset P as DAG and oDAG is given. The dim 2 poset such that its Hasse diagram coincide with digraf of P is constructed.

math.CO↗
arXiv2007

Bernoulli-Taylor formula in the case of Q-umbral Calculus

In this note we derive the Q-difference Bernoulli-Taylor formula with the rest term of the Cauchy form by the Viskov's method. This is an extension of technique by the use of Q-extented Kwasniewski's *-product . The main theorems of Q-umbral calculus were given by G. Markowsky in 1968 and extented by A.K.Kwasniewski.

math.GM↗