Geodesic
Locally restricted compositions. IV. Nearly free large parts and gap-freeness
Edward A. Bender1 ; E. Rodney Canfield2 ; Zhicheng Gao3
1University of California, San Diego
2University of Georgia
3Carleton University
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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We define the notion of asymptotically free for locally restricted compositions, which means roughly that large parts can often be replaced by any larger parts. Two well-known examples are Carlitz and alternating compositions. We show that large parts have asymptotically geometric distributions. This leads to asymptotically independent Poisson variables for numbers of various large parts. Based on this we obtain asymptotic formulas for the probability of being gap free and for the expected values of the largest part, number of distinct parts and number of parts of multiplicity $k$, all accurate to $o(1)$.
DOI : 10.37236/2571
Classification : 05A15, 05A16
Mots-clés : compositions, asymptotics

Edward A. Bender  1   ; E. Rodney Canfield  2   ; Zhicheng Gao  3

1 University of California, San Diego
2 University of Georgia
3 Carleton University 
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     author = {Edward A. Bender and E. Rodney Canfield and Zhicheng Gao},
     title = {Locally restricted compositions. {IV.} {Nearly} free large parts and gap-freeness},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {4},
     doi = {10.37236/2571},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/2571/}
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Edward A. Bender; E. Rodney Canfield; Zhicheng Gao. Locally restricted compositions. IV. Nearly free large parts and gap-freeness. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2571

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