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Explicit Formulae for Some Sums of Trinomial Coefficients |
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| รหัสดีโอไอ | |
| Creator | Yanapat Tongron |
| Title | Explicit Formulae for Some Sums of Trinomial Coefficients |
| Contributor | Takao Komatsu |
| Publisher | คณะวิทยาศาสตร์และเทคโนโลยี มหาวิทยาลัยเทคโนโลยีราชมงคลธัญบุรี |
| Publication Year | 2563 |
| Journal Title | วารสารวิทยาศาสตร์และเทคโนโลยี มทร.ธัญบุรี |
| Journal Vol. | 10 |
| Journal No. | 1 |
| Page no. | 161-169 |
| Keyword | sum, trinomial coefficient, cube root of unity, matrix |
| URL Website | http://www.sci.rmutt.ac.th/stj |
| Website title | Science and Technology RMUTT Journal |
| ISSN | 2229-1547 |
| Abstract | For ??,??,???{0,1,2},????,?????+??+??, and ?????+??+?? (mod 3), explicit formulae for ????????(??)??(??+??+??)!??!??!??!??????,?????,????? (mod 3), where the sum is over all non-negative integers ??,??,?? such that ??=??+??+??, are established by Carlitz [1] via properties of the cube root of unity. In this paper, another method to get these formulae is presented. Almost all ????????(??) are also expressed in terms of the cube root of unity. Mathematics Subject Classification: 05A10, 11B65 |
