Euler-type recurrences for t-color and t-regular partition functions

2024/12/18 by Bhowmik, Tapas, Tsai, Wei-Lun, Ye, Dongxi · 1 citation
#05A17 #11F11 #11F25 #11P81 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.14344

Abstract

We give Euler-like recursive formulas for the t-colored partition function when t=2 or t=3, as well as for all t-regular partition functions. In particular, we derive an infinite family of ``triangular number" recurrences for the 3-colored partition function. Our proofs are inspired by the recent work of Gomez, Ono, Saad, and Singh on the ordinary partition function and make extensive use of q-series identities for (q;q)_∞ and (q;q)_∞³.

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