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On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem

Iliev, Valentin — 2000

Serdica Mathematical Journal

Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube...

Isomerism as Manifestation of Intrinsic Symmetry of Molecules: Lunn–Senior’s Theory

Iliev, Valentin — 2009

Serdica Journal of Computing

This article presents the principal results of the doctoral thesis “Isomerism as internal symmetry of molecules” by Valentin Vankov Iliev (Institute of Mathematics and Informatics), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 15 December, 2008. This paper is an extended review of our doctoral thesis “Isomerism as Intrinsic Symmetry of Molecules” in which we present, continue, generalize, and trace out Lunn–Senior’s theory...

On some Finite-Dimensional Representations of Artin Braid Group Върху някои крайномерни представяния на групата на Артин на плитките

Iliev, Valentin — 2011

Union of Bulgarian Mathematicians

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими...

Semi-Symmetric Algebras: General Constructions. Part II

Iliev, Valentin Vankov — 2010

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 15A69, 15A78. In [3] we present the construction of the semi-symmetric algebra [χ](E) of a module E over a commutative ring K with unit, which generalizes the tensor algebra T(E), the symmetric algebra S(E), and the exterior algebra ∧(E), deduce some of its functorial properties, and prove a classification theorem. In the present paper we continue the study of the semi-symmetric algebra and discuss its graded dual, the corresponding canonical...

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