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**
Alternating Sums in the Hosoya Polynomial Triangle
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Rigoberto Flórez

Department of Mathematics and Computer Science

The Citadel

Charleston, SC 29409

USA

Robinson A. Higuita

Instituto de Matemáticas

Universidad de Antioquia

Medellín

Colombia

Antara Mukherjee

Department of Mathematics and Computer Science

The Citadel

Charleston, SC 29409

USA

**Abstract:**

The *Hosoya polynomial triangle* is a triangular arrangement of
polynomials where each entry is a product of two polynomials. The
geometry of this triangle is a good 1 tool to study the algebraic
properties of polynomial products. In particular, we find closed
formulas for the alternating sum of products of polynomials such as
Fibonacci polynomials, Chebyshev polynomials, Morgan-Voyce polynomials,
Lucas polynomials, Pell polynomials, Fermat polynomials, Jacobsthal
polynomials, and other familiar sequences of polynomials.

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(Concerned with sequences
A001109
A001906
A002450
A004190
A007655
A007954
A016153
A029547
A049660
A049668
A078987
A097316
A097725
A097728
A097731
A097734
A097737
A097740
A097778
A097781
A097836
A097839
A102902
A173205.)

Received April 4 2014;
revised version received August 20 2014.
Published in *Journal of Integer Sequences*, September 3 2014.

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