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

School of Natural Sciences

Duksung Women's University
Yonsei University

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
State	Published - 1 Jun 2024

Keywords

Partition
color partition
multi-Gaussian polynomial

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10.1142/S1793042124500659

Cite this

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title = "Multi-partition analogue of q-binomial coefficients",

abstract = "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.",

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AU - Kim, Byungchan

AU - Nam, Hayan

AU - Yu, Myungjun

PY - 2024/6/1

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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

UR - https://www.scopus.com/pages/publications/85190111528

U2 - 10.1142/S1793042124500659

DO - 10.1142/S1793042124500659

M3 - Article

AN - SCOPUS:85190111528

SN - 1793-0421

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SP - 1327

EP - 1351

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 5

ER -

Multi-partition analogue of q-binomial coefficients

Abstract

Keywords

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