DOAJ Open Access 2012

Locally Restricted Compositions IV. Nearly Free Large Parts and Gap-Freeness

Edward Bender Rodney Canfield Zhicheng Gao

Lihat Sumber DOI

Abstrak

We define the notion of $t$-free for locally restricted compositions, which means roughly that if such a composition contains a part $c_i$ and nearby parts are at least $t$ smaller, then $c_i$ can be replaced by any larger part. 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 and number distinct parts, all accurate to $o(1)$.

Topik & Kata Kunci

Mathematics

Penulis (3)

Edward Bender

Rodney Canfield

Zhicheng Gao

Format Sitasi

APA MLA BibTeX

Bender, E., Canfield, R., Gao, Z. (2012). Locally Restricted Compositions IV. Nearly Free Large Parts and Gap-Freeness. https://doi.org/10.46298/dmtcs.2997

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2997

Informasi Jurnal

Tahun Terbit: 2012
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2997
Akses: Open Access ✓