Mircea Merca

A new paper about truncated pentagonal number series

https://doi.org/10.3390/axioms12060514

A q-Series Congruence Inspired by Andrews and Ramanujan For each s∈{1,3,5}, we consider Rs(n) to be the number of the partitions of n into parts not congruent to 0, ±s(mod12). In recent years, some relations for computing the value of R3(n) were studied. In this paper, we investigate the parity of Rs(n) when s∈{1,5} and derive the following congruen...

https://www.scientificbulletin.upb.ro/rev_docs_arhiva/rez2ea_807050.pdf

www.scientificbulletin.upb.ro

https://doi.org/10.3390/axioms12020126

From Symmetric Functions to Partition Identities In this paper, we show that some classical results from q-analysis and partition theory are specializations of the fundamental relationships between complete and elementary symmetric functions.

https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/volume-27/issue-1/New-Combinatorial-Interpretations-for-the-Partitions-into-Odd-Parts-Greater/10.11650/tjm/220902.full

New Combinatorial Interpretations for the Partitions into Odd Parts Greater than One In this paper, we consider $Q_1(n)$ to be the number of partitions of $n$ into odd parts greater than one and provide new combinatorial interpretations for $Q_1(n)$. New linear relations involving Euler's partition function $p(n)$ and the overpartition function $\overline{p}(n)$ are obtained in this...

On the Ramanujan-type congruences modulo 8 for the overpartitions into odd parts Let denote the number of overpartitions of n into odd parts. In this paper, we provide a complete characterization of Ramanujan-type congruences modulo 8 for the overpartition function considerin...

Dyson’s crank and unimodal compositions - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas The crank is a partition statistic requested by Dyson in 1944 in order to combinatorially prove a Ramanujan congruence for Euler’s partition function p(n). In this paper, we provide connections between Dyson’s crank and unimodal compositions. Somewhat unrelated, we give a combinatorial proof of ...

A reversal of Schur’s partition theorem - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Let $$S_1$$ S 1 and $$S_2$$ S 2 be two subsets of the positive integers. G. E. Andrews called $$(S_1,S_2)$$ ( S 1 , S 2 ) an Euler pair whenever $$q(S_1;n)=p(S_2;n)$$ q ( S 1 ; n ) = p ( S 2 ; n ) for all positive integers n, where q(S; n) denotes the number of partitions of n into distinct parts ta...

Ramanujan-type congruences modulo 4 for partitions into distinct parts

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A further look at cubic partitions - The Ramanujan Journal The partitions in which even parts come in two colours are known as cubic partitions. In this paper, we introduce and investigate the cubic partition function A(n) which is defined as the difference between the number of cubic partitions of n into an even numbers of parts and the number of cubic par...

On Two Truncated Quintuple Series Theorems We investigate two truncated series derived recently by S. H. Chan, T. P. N. Ho, and R. Mao from the Watson quintuple product identity and experimentally discover two stronger results. In this cont...

Families of Ramanujan-Type Congruences Modulo 4 for the Number of Divisors In this paper, we explore Ramanujan-type congruences modulo 4 for the function σ0(n), counting the positive divisors of n. We consider relations of the form σ08(αn+β)+r≡0(mod4), with (α,β)∈N2 and r∈{1,3,5,7}. In this context, some conjectures are mad...