The vertex boundary-width problem (for short VBWP) is to determine the value of vbw(G)=max1 |V |minS⊆V,|S|= |N(S)| for a given graph G= (V ,E), where N(S)= {v / ∈ S|v is a neighbor of u for some u ∈ S}. In this paper, we give a lower bound for vertex boundary-width of complete k-ary trees. © 2007 Elsevier B.V. All rights reserved.

We construct an $(\infty,2)$-version of the (lax) Gray tensor product. On 1-categorical level, this is a binary (or more generally $n$-ary) functor on category $\Theta_2$-sets, and it shown to be left Quillen with respect Ara's model structure. Moreover we prove that product forms part "homotopical" (biclosed) monoidal structure, or precisely normal lax structure associative up homotopy.

Following [1], in this note we compute the average number of protected points in all k-ary trees with n internal points.

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

In this paper, we determine the expectation and variance of Xn the external path length in a random recursive k-ary tree of size n.

We study the recognition problem in the metaprogramming of finite normal predicate logic programs. That is, let L be a computable first order predicate language with infinitely many constant symbols and infinitely many n-ary predicate symbols and n-ary function symbols for all n ≥ 1. Then we can effectively list all the finite normal predicate logic programs Q0, Q1, . . . over L. Given some pro...

In this paper, we think about a correspondence framework that uses M-ary stage movement keying (MPSK), M-ary quadrature adequacy balance (MQAM), M-ary differential stage movement keying (MDPSK) and M-ary beat sufficiency regulation (MPAM) to transmit data over a Rayleigh blurring channel annoyed by added substance white Gaussian commotion (AWGN). This paper considers the execution of a double j...

Functions of type are characteristic functions on -ary relations. Keenan established their importance for natural language semantics, by showing that natural language has many examples of irreducible type functions, i.e. functions of type that cannot be represented as compositions of unary functions. Keenan proposed some tests for reducibility, and Dekker improved on these by proposing an invar...

Functions of type 〈n〉 are characteristic functions on n-ary relations. Keenan [5] established their importance for natural language semantics, by showing that natural language has many examples of irreducible type 〈n〉 functions, i.e., functions of type 〈n〉 that cannot be represented as compositions of unary functions. Keenan proposed some tests for reducibility, and Dekker [3] improved on these...

A group G (with additively written, not necessarily commutative group operation and neutral element 0) is called an H-group if there is a certain system Cl of w-ary algebraic operations (for certain natural numbers n) besides the addition such that for each w-ary operation OJEQ the condition 00... 0w = 0 (with n zeros on the left side) is satisfied. An important concept is that of an Q-ideal in...