Determinant formulas of some Toeplitz-Hessenberg matrices with Catalan entries

被引：6
作者：
Goy, Taras [1 ]
Shattuck, Mark [2 ,3 ]
机构：
[1] Vasyl Stefanyk Precarpathian Natl Univ, Fac Math & Comp Sci, UA-76018 Ivano Frankivsk, Ukraine
[2] Ton Duc Thang Univ, Inst Computat Sci, Ho Chi Minh City, Vietnam
[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
来源：
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2019年 / 129卷 / 04期
关键词：
Toeplitz-Hessenberg matrix; Catalan number; Trudi formula; generating function; 15A15; 15B05; 05A15;
D O I：
10.1007/s12044-019-0513-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider determinants of some families of Toeplitz-Hessenberg matrices having various translates of the Catalan numbers for the nonzero entries. These determinant formulas may also be rewritten as identities involving sums of products of Catalan numbers and multinomial coefficients. Combinatorial proofs may be given for several of the identities that are obtained.
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页数：17
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