Multi-partition analogue of q-binomial coefficients

Byungchan Kim; Hayan Nam; Myungjun Yu

doi:10.1142/S1793042124500659

Multi-partition analogue of q-binomial coefficients

Byungchan Kim, Hayan Nam, Myungjun Yu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce the multi-Gaussian polynomial G_k(M,N), a multi-partition analogue of the Gaussian polynomial (also known as q-binomial coefficient), as the generating function for certain restricted multi-color partitions. We study basic properties of multi- Gaussian polynomials and non-symmetric properties of G_k(M,N). We also derive a Sylvester-type identity and its application.

Original language	English
Pages (from-to)	1327-1351
Number of pages	25
Journal	International Journal of Number Theory
Volume	20
Issue number	5
DOIs	https://doi.org/10.1142/S1793042124500659
Publication status	Published - 2024 Jun 1

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© 2024 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042124500659

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N2 - We introduce the multi-Gaussian polynomial Gk(M,N), a multi-partition analogue of the Gaussian polynomial (also known as q-binomial coefficient), as the generating function for certain restricted multi-color partitions. We study basic properties of multi- Gaussian polynomials and non-symmetric properties of Gk(M,N). We also derive a Sylvester-type identity and its application.

AB - We introduce the multi-Gaussian polynomial Gk(M,N), a multi-partition analogue of the Gaussian polynomial (also known as q-binomial coefficient), as the generating function for certain restricted multi-color partitions. We study basic properties of multi- Gaussian polynomials and non-symmetric properties of Gk(M,N). We also derive a Sylvester-type identity and its application.

KW - Partition

KW - color partition

KW - multi-Gaussian polynomial

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ER -

Multi-partition analogue of q-binomial coefficients

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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