Refining Enumeration Schemes to Count According to Permutation Statistics
نویسندگان
چکیده
منابع مشابه
Refining Enumeration Schemes to Count According to Permutation Statistics
We develop algorithmic tools to compute quickly the distribution of permutation statistics over sets of pattern-avoiding permutations. More specfically, the algorithms are based on enumeration schemes, the permutation statistics are based on the number of occurrences of certain vincular patterns, and the permutations avoid sets of vincular patterns. We prove that whenever a finite enumeration s...
متن کاملRefining Enumeration Schemes to Count According to Inversion Number
Enumeration schemes were developed by Zeilberger, Vatter, and Pudwell as automatable methods to enumerate the set of permutations of length n which avoid a set of patterns B, Sn(B). In this paper we show how their schemes may be refined to enumerate Sn(B) according to the inversion number of each permutation.
متن کاملRe ning enumeration schemes to count according to the inversion number Andrew
Abstract. Enumeration schemes were developed by Zeilberger, Vatter, and Pudwell as automatable methods to enumerate the set of permutations of length n which avoid a set of patterns B, Sn(B). In this paper we show how their schemes may be re ned to enumerate Sn(B) according to the inversion number of each permutation. Mathematics Subject Classi cation(2000). 05A05, 05A15, 05A30, 68R15.
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The enumeration of permutations by inversions often leads to a q-analog of the usual generating 'nnetic,n. In this paper, two generalizations of the Worpitzky identity for the Eulerian numbers are obtained and used to enumerate permutations by the descent number and the major index of their inverses. The resulting (t, q)-generating series do in fact generalize the q-series obtainc? when countin...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/4002