Q-counting rook configurations and a formula of frobenius
نویسندگان
چکیده
منابع مشابه
A p, q-analogue of a Formula of Frobenius
Garsia and Remmel (JCT. A 41 (1986), 246-275) used rook configurations to give a combinatorial interpretation to the q-analogue of a formula of Frobenius relating the Stirling numbers of the second kind to the Eulerian polynomials. Later, Remmel and Wachs defined generalized p, q-Stirling numbers of the first and second kind in terms of rook placements. Additionally, they extended their definit...
متن کاملRepresentation theory of q-rook monoid algebras
We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.
متن کاملCounting Triangulations of Configurations
Calculating the number of Euclidean triangulations of a convex polygon P with vertices in a finite subset C ⊂ R2 containing all vertices of P seems to be difficult and has attracted some interest, both from an algorithmic and a theoretical point of view, see for instance [1], [2], [3], [4], [5], [7], [9], [10], [11]. The aim of this paper is to describe a class of configurations, convex near-go...
متن کاملCharacter Formulas for q-Rook Monoid Algebras
The q-rook monoid Rn(q) is a semisimple C(q)-algebra that specializes when q → 1 to C[Rn], where Rn is the monoid of n × n matrices with entries from {0, 1} and at most one nonzero entry in each row and column. We use a Schur-Weyl duality between Rn(q) and the quantum general linear group Uqgl(r ) to compute a Frobenius formula, in the ring of symmetric functions, for the irreducible characters...
متن کاملp-Rook Numbers and Cycle Counting in Cp o Sn
Cycle-counting rook numbers were introduced by Chung and Graham [8]. Cycle-counting q-rook numbers were introduced by Ehrenborg, Haglund, and Readdy [10] and cycle-counting q-hit numbers were introduced by Haglund [14]. Briggs and Remmel [5] introduced the theory of p-rook and p-hit numbers which is a rook theory model where the rook numbers correspond to partial permutations in Cp oSn, the wre...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90083-x