Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.6

On The Pfaffians and Determinants of Some Skew-Centrosymmetric Matrices


Fatih Yılmaz
Polatlı Arts and Sciences Faculty
Gazi University
06900 Ankara
Turkey

Tomohiro Sogabe
Graduate School of Engineering
Nagoya University
Nagoya, 464-8603
Japan

Emrullah Kırklar
Polatlı Arts and Sciences Faculty
Gazi University
06900 Ankara
Turkey

Abstract:

This paper shows that the Pfaffians and determinants of some skew centrosymmetric matrices can be computed by a paired two-term recurrence relation, or a general number sequence of second order. As a result, the complexities of the formulas are of order n. Furthermore, the formulas have no divisions at all, i.e., they fall into the class of breakdown-free algorithms.

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(Concerned with sequences A000045 A000129 A001045.)

Received June 20 2016; revised versions received July 8 2016; January 18 2017; February 2 2017. Published in Journal of Integer Sequences, February 11 2017.

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