Search results for "combinatoric"
showing 10 items of 1776 documents
Kernel theorems in the setting of mixed nonquasi-analytic classes
2008
Abstract Let Ω 1 ⊂ R r and Ω 2 ⊂ R s be nonempty and open. We introduce the Beurling–Roumieu spaces D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) , D ( M , M ′ } ( Ω 1 × Ω 2 ) and obtain tensor product representations of them. This leads for instance to kernel theorems of the following type: every continuous linear map from the Beurling space D ( ω 1 ) ( Ω 1 ) (respectively D ( M ) ( Ω 1 ) ) into the strong dual of the Roumieu space D { ω 2 } ( Ω 2 ) (respectively D { M ′ } ( Ω 2 ) ) can be represented by a continuous linear functional on D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) (respectively D ( M , M ′ } ( Ω 1 × Ω 2 ) ).
Classification of n-dimensional subvarieties of G(1, 2n) that can be projected to G(1, n + 1)
2005
A structure theorem is given for n-dimensional smooth subvarieties of the Grassmannian G(1, N); with N >= n + 3, that can be isomorphically projected to G(1, n + 1). A complete classification in the cases N = 2n + 1 and N = 2n follows, as a corollary.
The minimum size of fully irregular oriented graphs
2001
Abstract Digraphs in which any two vertices have different pairs of semi-degrees are called fully irregular. For n-vertex fully irregular oriented graphs (i.e. digraphs without loops or 2-dicycles) the minimum size is presented.
Invariant characters and coprime actions on finite nilpotent groups
2000
Suppose that a group A acts via automorphisms on a nilpotent group G having coprime order. Given an A-invariant character \(\chi \in {\rm Irr}(G)\), we show that the A-primitive irreducible characters that induce \(\chi \) from an A-invariant subgroup of G all have equal degree. We use this result to obtain some information about the characters of groups of p-length 1.
A matrix of combinatorial numbers related to the symmetric groups
1979
For permutation groups G of finite degree we define numbers t"B(G)=|G|^-^[email protected]?"R"@?"[email protected]?"1(1a"1(g))^b^"^i, where B=(b"1,...,b"1) is a tuple of non-negative integers and a"1(g) denotes the number of i cycles in the element g. We show that t"B(G) is the number of orbits of G, acting on a set @D"B(G) of tuples of matrices. In the case G=S"n we get a natural interpretation for combinatorial numbers connected with the Stiring numbers of the second kind.
On lazy representations and Sturmian graphs
2011
In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several properties of the representations of the natural integers in this numeration system.
Symmetric identities in graded algebras
1997
Let P k be the symmetric polynomial of degree k i.e., the full linearization of the polynomial x k . Let G be a cancellation semigroup with 1 and R a G-graded ring with finite support of order n. We prove that if R 1 satisfies $ P_k \equiv 0 $ then R satisfies $ P_{kn} \equiv 0 $ .
Subvarieties of the Varieties Generated by the SuperalgebraM1, 1(E) orM2(𝒦)
2003
Abstract Let 𝒦 be a field of characteristic zero, and let us consider the matrix algebra M 2(𝒦) endowed with the ℤ2-grading (𝒦e 11 ⊕ 𝒦e 22) ⊕ (𝒦e 12 ⊕ 𝒦e 21). We define two superalgebras, ℛ p and 𝒮 q , where p and q are positive integers. We show that if 𝒰 is a proper subvariety of the variety generated by the superalgebra M 2(𝒦), then the even-proper part of the T 2-ideal of graded polynomial identities of 𝒰 asymptotically coincides with the even-proper part of the graded polynomial identities of the variety generated by the superalgebra ℛ p ⊕ 𝒮 q . This description also affords an even-asymptotic desc…
Graphes connexes représentation des entiers et équirépartition
1983
Abstract Let q be an integer ≥2 and Ω a suitable subset of {0,…,q − 1}2; C (q; Ω) denotes the set of natural integers, the pairs of successive q-adic digits of which are in Ω. If P is an irrational polynomial, the sequence (P(n): n ∈ C (q; Ω)) is uniformly distributed modulo one.
On the Distribution ofB3-Sequences
1996
Abstract An infinite set of natural numbers is called aB3-sequence if all sumsa1+a2+a3withaj∈Aanda1⩽a2⩽a3are distinct. LetA(n) be the number of positive elements ⩽ninA. P. Erdos conjectures that everyB3-sequenceAsatisfies lim infn→∞ A(n) n−1/3=0. In this paper we prove that no sequence satisfyingA(n)∼αn1/3can be aB3-sequence. We also give other necessary conditions for aB3-sequence.