Number of right ideals and a q-analogue of indecomposable permutations
نویسندگان
چکیده
We prove that the number of right ideals of codimension n in the algebra of noncommutative Laurent polynomials in two variables over the finite field Fq is equal to (q − 1)q (n+1)(n−2) 2 ∑ θ q , where the sum is over all indecomposable permutations in Sn+1 and where inv(θ) stands for the number of inversions of θ. Mathematics Subject Classification Numbers: Primary: 05A15, Secondary: 05A19 Date: November 2, 2015. 1 2 ROLAND BACHER AND CHRISTOPHE REUTENAUER
منابع مشابه
ON ($epsilon, epsilon vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS
The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...
متن کاملIndecomposable permutations with a given number of cycles
A permutation a1a2 . . . an is indecomposable if there does not exist p < n such that a1a2 . . . ap is a permutation of {1, 2, . . . , p}. We compute the asymptotic probability that a permutation of Sn with m cycles is indecomposable as n goes to infinity with m/n fixed. The error term is O( log(n−m) n−m ). The asymptotic probability is monotone in m/n, and there is no threshold phenomenon: it ...
متن کاملON ( $alpha, beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS
Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...
متن کاملGENERALIZATION OF ($epsilon $, $epsilon $ $vee$ q)−FUZZY SUBNEAR-RINGS AND IDEALS
In this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. We have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. We have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...
متن کاملad-NILPOTENT b-IDEALS IN sl(n) HAVING A FIXED CLASS OF NILPOTENCE: COMBINATORICS AND ENUMERATION
We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of sl(n+1,C). We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the number of ideals having a given class of nilpotence. We study the relationships between these results and the combinatorics of Dyck paths, based upon a remarkable bijection between ad-nilpotent ideals an...
متن کامل