Some New Congruences For Partitions With Monochromatic Even Parts And Multichromatic Odd Parts
Congruences For Partitions With Monochromatic Even Parts And Multichromatic Odd Parts
Resumen
Let $a(n)$ denote the number of integer partitions of a positive integer $n$ wherein even parts appear in only one color (i.e. monochromatic) while the odd parts may appear in one of three colors (i.e. trichromatic). Hirschhorn and Sellers (2025) introduced a generalised version of $a(n)$ and defined the partition function $a_t(n)$ wherein even parts appear in one colour and odd parts may occur with one of the $t$ colours for any fixed positive integer $t$. They also proved some congruences modulo $7$ for $a_{7j+1}(n)$ for any integer $j\ge 1$. In this paper, we prove some new particular and infinite families of congruences for $a_t(n)$ by using $q$-series identities.
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Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
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