design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.

In this paper, an integrated machine scheduling withits due date setting problem has been considered. It is assumed that the machine is subject to some kind of random unavailability. Due dates should be set in an attractive and reliable manner, implying that they should be short and possible to be met. To this end, first, long due dates are penalized in the objective function. Then, for each cu...

One of the main techniques used in data mining is data clustering, which has many applications in computer science, biology, and social sciences. Constrained clustering is a type of clustering in which side information provided by the user is incorporated into current clustering algorithms. One of the well researched constrained clustering algorithms is called microaggregation. In a microaggreg...

In this paper we prove an extreme value law for a stochastic process obtained by iterating the Rényi map x ↦ β ( mod 1 ) , where assume that > is integer. Haiman (2018) derived recursion formula Lebesgue measure of threshold exceedance sets. We show how related to rescaled version k -generalized Fibonacci sequence. For latter sequence derive Binet which leads closed-form expression distribution...

There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of hypergraph as biadjacency graph. We use this to describe analyse rejection sampling algorithm for simple uniform with given degree sequence. Our uses, black box, an A graphs degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime depends on ...

For a sequence of positive integers s = (s1, . . . , sn), we define the rational lecture hall polytope R n . We prove that its h∗-polynomial, Q (s) n (x), has nonnegative integer coefficients that count certain statistics on s-inversion sequences. The polynomial Q n (x) can be viewed as an inflated version of the s-Eulerian polynomial, A n (x), associated with the integral lecture hall polytope...

We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space. The minimal-order recurrence for such a sequence is called the (non-commutative) A-polynomial of a knot. Using the method of guessing, we obtain this polynomial explicitly for the Kp = (−2, 3, 3+2p) pretzel knots for p = −5, . . . , 5. This is a particularly interesting family since the pairs (Kp,−K−p...

Let $s_0,s_1,s_2,\ldots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ polynomial function in $n$ if $s_n \ll \theta^n$ for some positive number $\theta$ satisfying $\theta < e^{1 + \tfrac{1}{2} \cdots+ \tfrac{1}{m}} -1$.