Delannoy Numbers and Preferential Arrangements

Kwang-Wu Chen
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Kwang-Wu Chen: Department of Mathematics, University of Taipei, Taipei 10048, Taiwan

Mathematics, 2019, vol. 7, issue 3, 1-9

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.

Keywords: preferential arrangements; Delannoy numbers; harmonic algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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