Congruences for an analogue of Lin's partition function

2025/10/15 by Guadalupe, Russelle
#05A17 #11P81 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.13685

Abstract

We study certain arithmetic properties of an analogue B(n) of Lin's restricted partition function that counts the number of partition triples π=(π₁,π₂,π₃) of n such that π₁ and π₂ comprise distinct odd parts and π₃ consists of parts divisible by 4. With the help of elementary q-series techniques and modular functions, we establish Ramanujan-type congruences modulo 2,3,5,7, and 9 for certain sums involving B(n).

Citations

• A note on congruences for the difference between even cranks and odd cranks
• From crank to congruences

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