• Three Dimensional Narayana and Schroder Numbers, preprint 2003 (ps) -- (pdf)
  

• Generalizing Narayana and Schroder Numbers to Higher Dimensions, Elect. J. Comb., vol. 11(1), Art. R54, 2004
  

• The 2^{n-1} factor for multi-dimensional lattice paths with diagonal steps, Sminaire Lotharingien de Combinatoire 2003(ps) -- (pdf)
  

• Objects counted by the Delannoy numbers, J. Integ. Seq., 2003
  

• Moments, Narayana Numbers, and the Cut and Paste for Lattice Paths, to appear in J. Stat. Planning and Inference in 2004(?) (ps) (pdf)
  

• Lattice Path Moments by Cut and Paste
  

• Bijective Recurrences for Motzkin Paths (To appear in Adv. in Appl. Math., 2001 (PostScript version)
  

• Counting Lattice Paths by Narayana Polynomials, Electronic Journal of Combinatorics, Vol. 7(1), R40, 2000
  

• Bijective Recurrences concerning Schroder Paths, Electronic Journal of Combinatorics, Vol. 5(1), 1998
  

• Schroder Triangles, Paths, and Parallelogram Polyominoes (with E. Pergola) in the Journal of Integer Sequences, Vol. 1 (1998), Article 98.1.7
  (PostScript version)
  

• Moments of generalized Motzkin paths.
  in the Journal of Integer Sequences, Vol. 3 (2000), Article 00.1.1

• A topography of Catalonia via Narayana statistics
  

• A proof about words without words
  

• Catalan Path Statistics having the Narayana Distribution
  This preprint investigates determining the statistics on the Catalan lattice paths satisfying the Narayana distribution. It extends the list of known statistics considerably and shows how the statistics relate to one another by moderately simple bijections.

• Constraint Sensitive Catalan Path Statistics having the Narayana Distribution
  

• Three Recurrences for Parallelogram Polyominoes
  

• Guessing, Ballot Numbers, and Refining Pascal's Triangle
  (1995) Given a shuffled deck of playing cards, consider drawing the top card, guessing its color, and discarding it face up. While always knowing the numbers of cards of each color remaining, repeat this until the deck is exhausted. If one does not guess deviously, what is the probability distribution for the number of wrong guesses? Using lattice path notions, we find one such distribution, which is related to the refinement of the binomial coefficients as lists of ballot numbers. This solution leads to a refinement of Pascal's triangle. Comments on this draft are very welcome. Again, `thanks' to Curtis Mack.

• The Narayana Distribution (to appear in 2001 or 2) (PostScript version)