منابع مشابه
Higher order peak algebras
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection...
متن کاملColoured peak algebras and Hopf algebras
For G a finite abelian group, we study the properties of general equivalence relations on Gn = Gn Sn , the wreath product of G with the symmetric group Sn , also known as the G-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of kGn as well as graded connected Hopf subalgebras of ⊕ n≥o kGn . In particular we construct a G-colou...
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This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...
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The concept of soft sets, introduced by Molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...
متن کاملEnumerations for Permutations by Circular Peak Sets
The circular peak set of a permutation σ is the set {σ(i) | σ(i−1) < σ(i) > σ(i+1)}. In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let cpn(S) denote the number of the permutations of order n which have the circular peak set S. For the case with |S| = 0, 1, 2, we derive the explicit formulas for cpn(S). We also obtain some recurrence relations for th...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1982
ISSN: 0026-2285
DOI: 10.1307/mmj/1029002674