In this paper, we are interested in a special class of integer matrices, namely the power-product matrix, defined with two positive integers n and d. Each matrix element is computed by weak compositions d into parts. The has several interesting applications such as power-sum representation polynomials difference-of-convex-sums-of-squares decomposition polynomials. We investigate some properties...

In full-knowledge multi-robot adversarial patrolling, a group of robots has to detect an adversary who knows the robots' strategy. The can easily take advantage any deterministic patrolling strategy, which necessitates employment randomised While Markov decision process been dominant methodology in computing penetration detection probabilities on polylines, we apply enumerative combinatorics ch...

My mathematical interests lie mainly in the field of combinatorics and how combinatorics can be used to prove algebraic identities. My current research is in the area of enumerative and algebraic combinatorics with an emphasis on counting the number of patterns which occur in words and permutations. This has been a very active area of research in recent years and there is a yearly conference, P...

Relations between the mean values of distributions flipped spins on periodic Heisenberg XX chain and some aspects enumerative combinatorics are discussed. The Bethe vectors, which state-vectors model, considered both as on- off-shell. It is this approach that makes it possible to represent study correlation functions in form non-intersecting nests lattice walks related plane partitions. We dist...

The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects constructed from vector spaces over finite fields. Examples of these objects include subspaces, flags of subspaces, direct sum decompositions, and linear maps ...

The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects constructed from vector spaces over finite fields. Examples of these objects include subspaces, flags of subspaces, direct sum decompositions, and linear maps ...

The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (EC)\citep{book:Stanley-2011} is a natural setting for spin composition, and easily leads to very general analytic formulae -- many of which hitherto not present in the literature. Based on it, we propose three general methods for computing spin multip...

The main thrust of my research is the use of techniques from information theory, probability and combinatorics to study structural, enumerative and algorithmic aspects of graph homomorphisms and related models, both in particular instances (independent sets and colorings, for example) and in general. Graph homomorphisms are important objects in graph theory, where they generalize a number of ce...

Unitary matrix integrals over symmetric polynomials play an important role in a wide variety of applications, including random theory, gauge number and enumerative combinatorics. We derive novel results on such apply these other identities to correlation functions long-range walks (LRRW) consisting hard-core bosons. generalize identity due Diaconis Shahshahani which computes unitary products po...