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2017 A generalization of Eulerian numbers via rook placements
Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf, Scarlitte Ponce
Involve 10(4): 691-705 (2017). DOI: 10.2140/involve.2017.10.691

Abstract

We consider a generalization of Eulerian numbers which count the number of placements of cn rooks on an n × n chessboard where there are exactly c rooks in each row and each column, and exactly k rooks below the main diagonal. The standard Eulerian numbers correspond to the case c = 1. We show that for any c the resulting numbers are symmetric and give generating functions of these numbers for small values of k.

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Esther Banaian. Steve Butler. Christopher Cox. Jeffrey Davis. Jacob Landgraf. Scarlitte Ponce. "A generalization of Eulerian numbers via rook placements." Involve 10 (4) 691 - 705, 2017. https://doi.org/10.2140/involve.2017.10.691

Information

Received: 26 April 2016; Accepted: 11 July 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 1359.05007
MathSciNet: MR3630311
Digital Object Identifier: 10.2140/involve.2017.10.691

Subjects:
Primary: 05A15

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2017
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