Vol. 10, No. 4, 2017

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ISSN: 1944-4184 (e-only)
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A generalization of Eulerian numbers via rook placements

Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf and Scarlitte Ponce

Vol. 10 (2017), No. 4, 691–705
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.

Keywords
Eulerian numbers, juggling, recursion, multiplex
Mathematical Subject Classification 2010
Primary: 05A15
Milestones
Received: 26 April 2016
Accepted: 11 July 2016
Published: 7 March 2017

Communicated by Jim Haglund
Authors
Esther Banaian
College of St. Benedict
Collegeville, MN 56321
United States
Steve Butler
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Christopher Cox
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
United States
Jeffrey Davis
Department of Mathematics and Computer Science
Emory University
Atlanta, GA 30322
United States
Jacob Landgraf
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
United States
Scarlitte Ponce
Department of Mathematics
Iowa State University
Ames, IA 50011
United States