Statistical Structure of Concave Compositions
نویسندگان
چکیده
In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure compositions including distribution perimeter tilt, number summands, shape graph a typical composition. We present solutions to these applying Fristedt’s conditioning device on uniform measure.
منابع مشابه
Concave Compositions
Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function disco...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2021
ISSN: ['0219-3094', '0218-0006']
DOI: https://doi.org/10.1007/s00026-021-00543-6