ARITHMETIC PROPERTIES SATISFIED BY A RECENT INTEGER PARTITION FUNCTION OF DOMBOS

Abstract The set of integer partitions of n , wherein the parts are either divisible by 4 or congruent to ± 1 ( mod 6 ) $\pm 1 \pmod {6}$ plus or minus 1 left parenthesis mod 6 right parenthesis , arose in a natural way in work of Dombos [‘A new grounded partition identity of type D 4 ( 3 ) $D_4^{(3)}$ upper D 4 Superscript left parenthesis 3 right parenthesis ’, SIGMA 22 (2026), Article no. 042]. Denote the function that counts the number of such partitions of n by dp ( n ) $\mathit {dp}(n)$ italic dp left parenthesis n right parenthesis . Using elementary generating function manipulations and classical q -series results, we prove several congruences satisfied by dp ( n ) $\mathit {dp}(n)$ italic dp left parenthesis n right parenthesis . As an example, we prove that, for all α ≥ 1 $\alpha \geq 1$ alpha greater than or equals 1 and all n ≥ 0 $n \geq 0$ n greater than or equals 0 , d p ( 3 2 α