A cycle lemma for permutation inversions |
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| Authors: | S Brunetti A Del Lungo |
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| Institution: | a Dipartimento di Matematica e Informatica Teorica, Università di Siena, Via del Capitano 15, 53100 Siena, Italy
b DSI, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy |
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| Abstract: | In this paper we study some properties of the inversion statistic. Some enumerative results concerning the permutations of the multiset {x1m1,x2m2} with respect to the inversion parameter are established and it is shown that these depend on gcd(m1,m2). Using a “cycle lemma”, a combinatorial proof of the results is given. Moreover, some applications to the Gaussian binomial coefficient are illustrated. |
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| Keywords: | Multiset Permutation Inversion Major Cyclic shift Greatest common divisor Congruence Gaussian binomial coefficient |
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