# Combinatorics

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**Combinatorics**Deciding whether or not a feasible solution to the Traveling Salesman Problem with Pickups and Deliveries (TSPPD) exists is polynomially solvable. We prove that counting the number of feasible solutions of the TSPPD is hard by showing the... more

In the present paper we define the notion of adjacency matrix and incidence matrix of a soft graph and derive some results regarding these matrices. We show that some of the classical results of graph theory does not hold for soft graphs.

In the Cluster Editing problem, a given graph is to be transformed into a disjoint union of cliques via a minimum number of edge editing operations. In this paper we introduce a new variant of Cluster Editing whereby a vertex can be... more

In this paper we are interested in the Cage Problem that consists in constructing regular graphs of given girth g and minimum order. We focus on girth g=5, where cages are known only for degrees k < 7. We construct regular graphs of... more

This article applies mathematical methods to investigating (extremely) simplified versions of the team selection problem for football managers. The team selection problem – obviously a game problem – is analysed game theoretically, but... more

We investigate paths in Bernoulli's triangles, and derive several relations linking the partial sums of binomial coefficients to the Fibonacci numbers.

The distinguishing number of a group $G$ acting faithfully on a set $V$ is the least number of colors needed to color the elements of $V$ so that no non-identity element of the group preserves the coloring. The distinguishing number of a... more

A group of permutations $G$ of a set $V$ is $k$-distinguishable if there exists a partition of $V$ into $k$ cells such that only the identity permutation in $G$ fixes setwise all of the cells of the partition. The least cardinal number... more

The following paper presents the research developed with students within USC School of Architecture as part of the Gamescapes Agenda, directed by Jose Sanchez.

The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^\rho \mathcal{I}^\alpha_{a+}f\big)(x) = \frac{\rho^{1- \alpha }}{\Gamma({\alpha})} \int^x_a... more

a presentation on property graph implementation

Impariamo a contare nell’infanzia ed è probabilmente per questo motivo che reputiamo il contare una delle attività matematiche più elementari. Questo è senz’altro vero quando gli oggetti da contare sono pochi, ma quando abbiamo a che fare... more

A set S of vertices in a graph G(V, E) is called a dominating set if every vertex v ∈ V is either an element of S or is adjacent to an element of S. A set S of vertices in a graph G(V, E) is called a total dominating set if every vertex v... more

One of the most popular methods to visualize the overlap and differences between data sets is the Venn diagram. Venn diagrams are especially useful when they are ‘area-proportional’ i.e. the sizes of the circles and the overlaps... more

In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and... more

WHY A MATHEMATICS OF UNCERTAINTY? - probabilities do not represent well ignorance and lack of data; - evidence is normally limited, rather than infinite as assumed by (frequentist) probability; - expert knowledge needs often to be... more

Kant and Aristotle reassesses the prevailing understanding of Kant as an anti-Aristotelian philosopher. Taking epistemology, logic, and methodology to be the key disciplines through which Kant’s transcendental philosophy stood as an... more

Free: Computer Science Unplugged (csunplugged.org) for K-12 Education (csunplugged.org). ￼￼￼ Many children and teachers have helped us to refine our ideas. The children and teachers at South Park School (Victoria, BC), Shirley Primary... more

Todas as versões desse trabalho estão disponíveis nessa aba clicando em "Files".

Created on June, 2011. Problems are taken from IMO, IMO Shortlist/Longlist, and some other famous math competitions.

It is a text book on the mathematical theory of production control. It is written in Hungarian.

The edge-chromatic number of the complete graph on n vertices, X'(Kn), is well-known and simple to find. This number has applications in round-robin tournaments and what we will call the "efficient handshake" problem: namely, it gives... more

Principio de Inclusión-Exclusión

Análisis Combinatorio

Análisis Combinatorio

In this paper we want to employ the different applications, especially those of linear algebra, onto our findings of the combinatorial number theory in order to get a better understanding of the Goldbach - and Landau hypothesis. We do... more

Análisis combinatorio, ejercicios de conteo

PLANARIDAD Y COLORACIONES Análisis Combinatorio

Sažetak: Tekst se bavi problemom odnosa Dekartovog projekta Mathesis universalis i Lajbnicovog univerzalnog jezika. Iako je u Lajbnicovo vreme postojalo već mnoštvo pokušaja da se razvije jedan takav jezik, ono što Lajbnica izdvaja u... more