Algebraic Polynomial Identities

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

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Graded polynomial identities for the upper triangular matrix algebra over a finite field

Journal of Algebra ◽

10.1016/j.jalgebra.2020.05.008 ◽

2020 ◽

Vol 559 ◽

pp. 625-645

Author(s):

Dimas José Gonçalves ◽

Evandro Riva

Keyword(s):

Finite Field ◽

Matrix Algebra ◽

Triangular Matrix ◽

Polynomial Identities ◽

Triangular Matrix Algebra ◽

Graded Polynomial Identities ◽

Upper Triangular Matrix

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Algebraic Polynomial Based Topological Study of Graphite Carbon Nitride (g-) Molecular Structure.

Polycyclic Aromatic Compounds ◽

10.1080/10406638.2021.1934044 ◽

2021 ◽

pp. 1-22

Author(s):

Abdul Rauf ◽

Muhammad Ishtiaq ◽

Mehwish Hussain Muhammad ◽

Muhammad Kamran Siddiqui ◽

Qammar Rubbab

Keyword(s):

Molecular Structure ◽

Algebraic Polynomial ◽

Carbon Nitride

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Approximation by Boolean sums of linear operators: Telyakovskiǐ-type estimates

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700028410 ◽

1990 ◽

Vol 42 (2) ◽

pp. 253-266 ◽

Cited By ~ 2

Author(s):

Jia-Ding Cao ◽

Heinz H. Gonska

Keyword(s):

Upper Bound ◽

Algebraic Polynomial ◽

Present Note ◽

Type Inequality ◽

Linear Operators ◽

Polynomial Operators ◽

Boolean Sums ◽

General Conditions

In the present note we study the question: “Under which general conditions do certain Boolean sums of linear operators satisfy Telyakovskiǐ-type estimates?” It is shown, in particular, that any sequence of linear algebraic polynomial operators satisfying a Timan-type inequality can be modified appropriately so as to obtain the corresponding upper bound of the Telyakovskiǐ-type. Several examples are included.

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