112 research outputs found
A bijection to count (1-23-4)-avoiding permutations
A permutation is (1-23-4)-avoiding if it contains no four entries, increasing
left to right, with the middle two adjacent in the permutation. Here we give a
2-variable recurrence for the number of such permutations, improving on the
previously known 4-variable recurrence. At the heart of the proof is a
bijection from (1-23-4)-avoiding permutations to increasing ordered trees whose
leaves, taken in preorder, are also increasing.Comment: latex, 16 page
Enumeration of a dual set of Stirling permutations by their alternating runs
In this paper, we count a dual set of Stirling permutations by the number of
alternating runs. Properties of the generating functions, including recurrence
relations, grammatical interpretations and convolution formulas are studied.Comment: 8 page
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