Let podℓ(n) and pedℓ(n) denote the number of ℓ-regular partitions of a positive integer n into distinct odd parts and the number of ℓ-regular partitions of a positive integer n into distinct even parts, respectively. Our first goal in this note was to prove two congruence relations for podℓ(n). Furthermore, we found a formula for the action of the Hecke operator on a class of eta-quotients. As two applications of this result, we obtained two infinite families of congruence relations for pod5(n). We also proved a congruence relation for pedℓ(n). In particular, we established a congruence relation modulo 2 connecting podℓ(n) and pedℓ(n).
Citation: JingJun Yu. Some congruences for ℓ-regular partitions with certain restrictions[J]. AIMS Mathematics, 2024, 9(3): 6368-6378. doi: 10.3934/math.2024310
| [1] | Marcella Reale . Annual Report 2020. AIMS Allergy and Immunology, 2021, 5(1): 33-37. doi: 10.3934/Allergy.2021003 |
| [2] | Marcella Reale, Xu Guo . Annual Report 2024. AIMS Allergy and Immunology, 2025, 9(1): 1-7. doi: 10.3934/Allergy.2025001 |
| [3] | Marcella Reale, Xu Guo . Annual Report 2023. AIMS Allergy and Immunology, 2024, 8(1): 1-7. doi: 10.3934/Allergy.2024001 |
| [4] | Marcella Reale . Annual Report 2022. AIMS Allergy and Immunology, 2023, 7(1): 40-44. doi: 10.3934/Allergy.2023003 |
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Let podℓ(n) and pedℓ(n) denote the number of ℓ-regular partitions of a positive integer n into distinct odd parts and the number of ℓ-regular partitions of a positive integer n into distinct even parts, respectively. Our first goal in this note was to prove two congruence relations for podℓ(n). Furthermore, we found a formula for the action of the Hecke operator on a class of eta-quotients. As two applications of this result, we obtained two infinite families of congruence relations for pod5(n). We also proved a congruence relation for pedℓ(n). In particular, we established a congruence relation modulo 2 connecting podℓ(n) and pedℓ(n).
Together with the Editorial Office of AIMS Allergy and Immunology, I wish to testify my sincere gratitude to all authors, members of the editorial board and reviewers, thanking everyone for their contribution to AIMS Allergy and Immunology in 2021.
It was the support of all members of our editorial board and peer reviewers that, despite of COVID-19 difficulties, made possible to successfully complete the full peer review, editing and publishing processes for AIMS Allergy and Immunology in 2021.
The submissions of our AIMS Allergy and Immunology journal in 2021 increased significantly, with 4 papers under processing (submitted in 2021); during this 2021 we had 50% acceptance/rejection ratio and publication time (from submission to online) was reduced from 70.4 days to 61 days, illustrating the strict and efficient review process. We have 10 top articles with highest citations from 5 (1 paper), 4 (3 papers), 3 (2 papers), 2 (4 papers), and many countries are represented among our authors.
An important part of our strategy has been preparation of special issues. In 2021, two special issues and four topical sections were planned. AIMS Allergy and Immunology has 67 members now, and 8 of which joined in 2021. We will continue to renew editorial board in 2022.
To promote and encourage submissions we have established the “Best Paper Award” and “Editorial board member of the year” for the editorial board member who introduced the largest number of researchers, authors of manuscripts accepted/published or in press.
The road is still long and winding but we hope that in 2022, with the support of all the members of the editorial board and reviewers, it will be possible to expand the number of papers submitted and accepted, to be able to publish the scientific contributions of the congresses and special issues organized by the members of the editorial board, to increase the citation/paper and total citations to get the academic rank of AIMS Allergy and Immunology as soon as possible.
Prof. Marcella Reale, Editor-in-Chief
AIMS Allergy and Immunology journal
Dept. of Innovative Technologies in Medicine and Dentistry
University “G. d'Annunzio” Chieti-Pescara
Via dei Vestini, Chieti, Italy
Under processing paper: 4
Rejection rate: 50%
Publication time (from submission to online): 61 days
| Type | Number |
| Review | 7 |
| Research article | 5 |
| Mini review | 3 |
| Letter | 2 |
| Communication | 1 |
| Commentary | 1 |
| Editorial | 1 |
The top 10 articles with highest viewed:
| Title | Viewed |
| Targeting cancer cells: from historic methods to modern chimeric antigen receptor (CAR) T-Cell strategies | 5719 |
| Immunological and toxicological effects of bad indoor air to cause Dampness and Mold Hypersensitivity Syndrome | 4748 |
| “Toll-free” pathways for production of type I interferons | 4329 |
| Toll-like receptors and immune cell crosstalk in the intestinal epithelium | 4122 |
| Main NK cell receptors and their ligands: regulation by microRNAs | 3952 |
| Interactions of allergic rhinitis and bronchial asthma at mucosal immunology level | 3581 |
| Basophil activation through TLR2 and TLR4 signaling pathways | 3531 |
| IL-10 in cancer: Just a classical immunosuppressive factor or also an immunostimulating one? | 3494 |
| Contribution of antibody-dependent enhancement to the pathogenesis of coronavirus infections | 3479 |
| CLEC receptors, endocytosis and calcium signaling | 3435 |
The top 10 articles with highest citations:
| Title | Citations |
| “Toll-free” pathways for production of type I interferons | 5 |
| Airborne exposure to laboratory animal allergens | 4 |
| CLEC receptors, endocytosis and calcium signaling | 4 |
| IL-10 in cancer: Just a classical immunosuppressive factor or also an immunostimulating one? | 4 |
| Main NK cell receptors and their ligands: regulation by microRNAs | 3 |
| Immunological and toxicological effects of bad indoor air to cause Dampness and Mold Hypersensitivity Syndrome | 3 |
| A recipe for myositis: nuclear factor κB and nuclear factor of activated T-cells transcription factor pathways spiced up by cytokines | 2 |
| Reducing dust and allergen exposure in bakeries | 2 |
| Co-inhibitory receptors in female asthmatic patients: Correlation with IL-17 and IL-26 | 2 |
| Basophil activation through TLR2 and TLR4 signaling pathways | 2 |
Topical section
Immunity to Viruses
https://www.aimspress.com/allergy/article/5830/special-articles
Special issue
The role of extracellular vesicles and miRNAs in allergy and immune tolerance
Special issue editor: Dr. Katarzyna Nazimek
https://www.aimspress.com/allergy/article/5855/special-articles
AIMS Allergy and Immunology has 67 members, and 8 of which joined in 2021.
In the fifth year of our journal, the journal developed much faster than before under the leadership of the Editor-in-Chief Prof. Marcella Reale. We have received 36 submissions and published 20 papers in 2021.
We reduce the publication time from 70.4 days to 61 days. Each submitted article is processed carefully, fairly, promptly, and the accepted papers appear in the journal in the shortest time.
Increase influence by soliciting and advertising high quality articles and special issues (topics).
We seek to be indexed by more databases in 2022.
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D. S. Gireesh, M. D. Hirschhorn, M. S. Mahadeva Naika, On 3-regular partitions with odd parts distinct, Ramanujan J., 44 (2017), 227–236. https://doi.org/10.1007/s11139-016-9814-0 doi: 10.1007/s11139-016-9814-0
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R. Drema, N. Saikia, Arithmetic properties for l-regular partition functions with distinct even parts, Bol. Soc. Mat. Mex., 28 (2022), 10–20. https://doi.org/10.1007/s11139-018-0044-5 doi: 10.1007/s11139-018-0044-5
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B. Hemanthkumar, H. S. Sumanth Bharadwaj, M. S. Mahadeva Naika, Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts, Acta Mathematica Vietnamica, 44 (2019), 797–811. https://doi.org/10.1007/s40306-018-0274-z doi: 10.1007/s40306-018-0274-z
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JingJun Yu. Some congruences for ℓ-regular partitions with certain restrictions[J]. AIMS Mathematics, 2024, 9(3): 6368-6378. doi: 10.3934/math.2024310
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