Formulæ for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz). The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for p m (n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.
Keywords for this software
References in zbMATH (referenced in 10 articles , 1 standard article )
Showing results 1 to 10 of 10.
- Castillo, Angelica; Flores, Stephanie; Hernandez, Anabel; Kronholm, Brandt; Larsen, Acadia; Martinez, Arturo: Quasipolynomials and maximal coefficients of Gaussian polynomials (2019)
- Cimpoeaş, Mircea; Nicolae, Florin: On the restricted partition function (2018)
- O’Sullivan, Cormac: Partitions and Sylvester waves (2018)
- Srdanov, Aleksa: Universal formulas for the number of partitions (2018)
- Dilcher, Karl; Vignat, Christophe: An explicit form of the polynomial part of a restricted partition function (2017)
- Choliy, Yuriy; Sills, Andrew V.: A formula for the partition function that “counts” (2016)
- Baldoni, Velleda; Berline, Nicole; De Loera, Jesús A.; Dutra, Brandon E.; Köppe, Matthias; Vergne, Michèle: Coefficients of Sylvester’s denumerant (2015)
- Martinjak, Ivica; Svrtan, Dragutin: Some families of identities for the integer partition function (2015)
- Baldoni, V.; Berline, N.; Dutra, B. E.; Köppe, M.; Vergne, M.: Top degree coefficients of the denumerant (2013)
- Sills, Andrew V.; Zeilberger, Doron: Formulæ for the number of partitions of (n) into at most (m) parts (using the quasi-polynomial ansatz) (2012)