Combinatorics and Graph Theory

2101 Submissions

[3] viXra:2101.0087 [pdf] submitted on 2021-01-14 05:21:03

The Theory of Closed Cell Packaging Fields

Authors: Franz Hermann
Comments: 38 Pages.

In the first part of our study, we give definitions, examples, and properties of the simplest numerical packings. The second part talks about packages related to number systems. In the third part, we will talk about packages whose period is a prime number
Category: Combinatorics and Graph Theory

[2] viXra:2101.0076 [pdf] submitted on 2021-01-12 07:01:07

Any Finite Connected Poset is Isomorphic to Aut(x)\x for Some Finite Poset X

Authors: Pierre-Yves Gaillard
Comments: 2 Pages.

We show that, given any finite connected poset X, there is a finite poset Y such that the quotient poset Aut(Y)\Y is isomorphic to X.
Category: Combinatorics and Graph Theory

[1] viXra:2101.0040 [pdf] submitted on 2021-01-06 08:02:03

On the Minimal Uncompletable Word Problem for Unambiguous Automata

Authors: Antonio Boccuto, Arturo Carpi
Comments: 11 Pages.

This paper deals with nite (possibly not complete) unambiguous automata, not necessarily deterministic. In this setting, we investigate the problem of the minimal length of the uncompletable word. This problem is associated with the well-known conjecture formulated by A. Restivo. We introduce the concept of relatively maximal row for a suitable set of matrices, and show the existence of a relatively maximal row of length of quadratic order with respect to the number of the states of the treated automaton. We give some estimates of the maximal length of the minimal uncompletable word in connection with the number the states of the involved automaton and the length of a suitable relatively maximal but not maximal word, provided that it exists. In the general case, we establish an estimate of the length of the minimal uncompletable word in terms of the number of states of the studied automaton, the length of a suitable relatively maximal word and the minimal length of the uncompletable word of the automaton formed by all associated maximal rows.
Category: Combinatorics and Graph Theory