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Some congruences for 3-component multipartitions

100%

Zhao T. Y., Jin L. J., Gu C.

Open Mathematics

2016

tom 14

nr 1

783-788

Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).

A note on the determinant of a Toeplitz-Hessenberg matrix

76%

Merca M.

Special Matrices

2013

tom 1

10-16

The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.

Ograniczanie wyników

1 Open Mathematics

1 Special Matrices

1 Gu C.

1 Jin L. J.

1 Merca M.

1 Zhao T. Y.

1 2016

1 2013

Wyniki wyszukiwania

Some congruences for 3-component multipartitions

A note on the determinant of a Toeplitz-Hessenberg matrix