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Major Index and Inversion Number of Permutations

✍ Scribed by Dominique Foata; Marcel-Paul Schützenberger

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
800 KB
Volume
83
Category
Article
ISSN
0025-584X

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📜 SIMILAR VOLUMES

The major index polynomial for conjugacy
The major index polynomial for conjugacy classes of permutations
✍ Michelle L. Wachs 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 628 KB

Garsia (1988) gives a remarkably simple expression for the major index enumerator for permutations of a fixed cycle type evaluated at a primitive root of unity. He asks for a direct combinatorial proof of this identity. Here we give such a combinatorial derivation.

A CAT algorithm for generating permutati
A CAT algorithm for generating permutations with a fixed number of inversions
✍ Scott Effler; Frank Ruskey 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 103 KB

We develop a constant amortized time (CAT) algorithm for generating permutations with a given number of inversions. We also develop an algorithm for the generation of permutations with given index.

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Cycle index of direct product of permutation groups and number of equivalence classes of subsets of Zv
✍ Wan-Di Wei; Ju-Yong Xu 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 460 KB

Let u be a positive integer and Z, the residue class ring modulo U. Two subsets D1 and D, of Z, are said to be equivalent if there exist t,seZ, with gcd(t, v)= 1 such that D, = tD, +s. We are interested in the number of equivalence classes of k-subsets of 2, and the number of equivalence classes of

Refined Stirling Numbers: Enumeration of
Refined Stirling Numbers: Enumeration of Special Sets of Permutations and Set-Partitions
✍ J. Katriel 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 110 KB

The refined Stirling numbers of the first kind specify the number of permutations of n indices possessing m i cycles whose lengths modulo k are congruent to i; i ¼ 0; 1; 2; . . . ; k À 1: The refined Stirling numbers of the second kind are similarly defined in terms of set-partitions and the cardi