A preferential arrangement of a set X n = {1, 2, . . . , n} is an orderedWe also propose conjectures on number of restricted barred preferential arrangements.
Mathematics Subject Classifications:05A18,05A19,05A16, 2013Keywords: Barred preferential arrangements, restricted barred preferential arrangements, restricted sections and free sections.
A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by making use of the generalised Stirling numbers proposed by Hsu and Shiue (1998). We discuss how these generalised barred preferential arrangements offer a unified combinatorial interpretation of geometric polynomials. We also discuss asymptotic properties of these numbers.Mathematics Subject Classifications : 05A15, 05A16, 05A18, 05A19, 11B73, 11B83 Keyword(s):preferential arrangement, barred preferential arrangement, geometric polynomial.
A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this study we examine combinatorial properties of barred preferential arrangements whose elements are colored with a number of available colors.
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