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Restricted Words by Adjacencies
Discrete Mathematics
  • Don Rawlings, California Polytechnic State University - San Luis Obispo
Publication Date

A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to refinements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation on compositions, (2) the enumeration of directed vertically convex polyominoes by upper descents, area, perimeter, relative height, and column number, (3) a tri-variate extension of MacMahon's determinant formula for permutations with prescribed descent set, and (4) a combinatorial setting for an entire sequence of bibasic Bessel functions.

Citation Information
Don Rawlings. "Restricted Words by Adjacencies" Discrete Mathematics Vol. 220 Iss. 1-3 (2000) p. 183 - 200
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