A condition for the existence of zero coefficients in the powers of the determinant polynomial

Autor:	Itoh, Minoru, Shimoyoshi, Jimpei
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics Mathematics - Representation Theory Primary 05B15 05B20 15A15 Secondary 11A41
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jalgebra.2021.03.017
Popis:	We discuss the existence of zero coefficients in the powers of the determinant polynomial of order $n$. D. G. Glynn proved that the coefficients of the $m$th power of the determinant polynomial are all nonzero, if $m = p-1$ with a prime $p$. We show that the converse also holds, if $n \geq 3$. The proof is quite elementary. Comment: 4 pages; to appear in J. Algebra
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.00838 Zobrazit plný text záznamu View this record from Arxiv