Geodesic
Greatest descents after any maxima in compositions
Margaret Archibald1 ; Aubrey Blecher1 ; Charlotte Brennan1 ; Arnold Knopfmacher1
1University of the Witwatersrand
The electronic journal of combinatorics, Tome 22 (2015) no. 4
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In this paper, compositions of $n$ are studied. These are sequences of positive integers $(\sigma_i)_{i=1}^k$ whose sum is $n$. We define a maximum to be a part which is greater than or equal to all other parts. We investigate the size of the descents immediately following any maximum and we focus particularly on the largest and average of these, obtaining the generating functions in each case. Using Mellin transforms, we obtain asymptotic expressions for these quantities.
DOI : 10.37236/5303
Classification : 05A15
Mots-clés : compositions, descents, generating functions, asymptotics, Mellin transforms

Margaret Archibald  1   ; Aubrey Blecher  1   ; Charlotte Brennan  1   ; Arnold Knopfmacher  1

1 University of the Witwatersrand 
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     title = {Greatest descents after any maxima in compositions},
     journal = {The electronic journal of combinatorics},
     year = {2015},
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     number = {4},
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Margaret Archibald; Aubrey Blecher; Charlotte Brennan; Arnold Knopfmacher. Greatest descents after any maxima in compositions. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5303

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