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Mathematics 2019, 7(3), 238; https://doi.org/10.3390/math7030238

Delannoy Numbers and Preferential Arrangements

Department of Mathematics, University of Taipei, Taipei 10048, Taiwan
Current address: No. 1, Ai-GuoWest Road, Taipei 10048, Taiwan.
Received: 25 January 2019 / Revised: 1 March 2019 / Accepted: 2 March 2019 / Published: 6 March 2019
(This article belongs to the Special Issue Special Functions and Applications)
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Abstract

A preferential arrangement on [ [ n ] ] = { 1 , 2 , , n } is a ranking of the elements of [ [ n ] ] where ties are allowed. The number of preferential arrangements on [ [ n ] ] is denoted by r n . The Delannoy number D ( m , n ) is the number of lattice paths from ( 0 , 0 ) to ( m , n ) in which only east ( 1 , 0 ) , north ( 0 , 1 ) , and northeast ( 1 , 1 ) steps are allowed. We establish a symmetric identity among the numbers r n and D ( p , q ) by means of algebraic and combinatorial methods. View Full-Text
Keywords: preferential arrangements; Delannoy numbers; harmonic algebras preferential arrangements; Delannoy numbers; harmonic algebras
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chen, K.-W. Delannoy Numbers and Preferential Arrangements. Mathematics 2019, 7, 238.

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