The purpose of this paper is to present some enumerative results concerning the class View the MathML sourcek of permutations of the multiset {1m1, 2m2,…,rmr} having inversion number congruent to k modulo n, with n = m1 + m2 + ··· + mr and 0 ≤ k < n. We show that the enumeration of this family of permutations is connected to gcd(m1, m2,…,mr), and if gcd(m1, m2,…,mr) = 1, then View the MathML source, for each 0 ≤ k < n. Finally, some applications of these properties concerning the q-multinomial coefficient are found.
Brunetti, S., DEL LUNGO, A., DEL RISTORO, F. (2001). An equipartition property for the distribution of multiset permutation inversions. ADVANCES IN APPLIED MATHEMATICS, 27, 41-50.
An equipartition property for the distribution of multiset permutation inversions.
BRUNETTI, SARA;DEL LUNGO, ALBERTO;
2001-01-01
Abstract
The purpose of this paper is to present some enumerative results concerning the class View the MathML sourcek of permutations of the multiset {1m1, 2m2,…,rmr} having inversion number congruent to k modulo n, with n = m1 + m2 + ··· + mr and 0 ≤ k < n. We show that the enumeration of this family of permutations is connected to gcd(m1, m2,…,mr), and if gcd(m1, m2,…,mr) = 1, then View the MathML source, for each 0 ≤ k < n. Finally, some applications of these properties concerning the q-multinomial coefficient are found.
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https://hdl.handle.net/11365/3039
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