Integer partitions with restricted odd and even parts

Nipen Saikia ()
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Nipen Saikia: Rajiv Gandhi University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1230-1234

Abstract: Abstract In this note, two generalized partition functions $$p_o^\alpha (n)$$ p o α ( n ) and $$p_e^\beta (n)$$ p e β ( n ) are considered, where for any odd positive integer $$\alpha $$ α , $$p_o^\alpha (n)$$ p o α ( n ) denotes the number of partitions of n into odd parts such that no parts is congruent to $$\alpha $$ α modulo $$2\alpha $$ 2 α , and for any even positive integer $$\beta $$ β , $$p_e^\beta (n)$$ p e β ( n ) denotes the number of partitions of n into even parts such that no parts is congruent to $$\beta $$ β modulo $$2\beta $$ 2 β . Some divisibility properties of $$p_o^\alpha (n)$$ p o α ( n ) and $$p_e^\beta (n)$$ p e β ( n ) are discussed for some particular values of $$\alpha $$ α and $$\beta $$ β .

Keywords: Integer partition; Partition with restricted odd and even parts; Congruence; q-series identities; 11P83; 05A17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-024-00584-6

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