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Leonard M. Smiley

Publications and source records attributed to Leonard M. Smiley.

2 recordsLinked to original sources
arXiv2000

Completion of a Rational Function Sequence of Carlitz

The exponential generating functions of {n^(n+m)} for arbitrary integer m are expressed as rational functions of the e.g.f. of {n^(n-1)} [the tree function] and then of the e.g.f. of {n^n} [the endofunction function]. The coefficients in these rational functions include 2nd-order Eulerian numbers (a result of L. Carlitz), 2nd-order Stirling numbers, and Stirling numbers of the first kind for negative sets (in the sense of D. Loeb). Several combinatorial identities follow.

math.CO↗
arXiv1999

Variants of Schroeder Dissections

Some formulae are given for the enumeration of certain types of dissections of the convex (n+2)-gon by non-crossing diagonals. The classical Schroeder and Motzkin numbers are addressed using a cataloguing tool, the "reversive symbol". The elementary details are referred to three Web addresses.

math.CO↗