The goal of this paper is to discuss congruences involving the function <mml:math alttext="$\overline {c\phi _m } \left( n \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mrow><mml:mi>c</mml:mi><mml:msub><mml:mi>&#981;</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="true">&#175;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>,
which denotes the number of generalized Frobenius partitions of <mml:math alttext="$n$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> with <mml:math alttext="$m$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math> colors whose order is
<mml:math alttext="$m$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math> under cyclic permutation of the <mml:math alttext="$m$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math> colors.

International Journal of Mathematics and Mathematical Sciences

Congruences involving generalized Frobenius partitions

Abstract

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