# Maurizio Monge

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**Maurizio Monge**,

an Italian mathematician and computer scientist, Ph.D. in 2012 from Scuola Normale Superiore di Pisa under supervision of Roberto Dvornicich ^{[2]}.
His research interests include extensions of local fields, Galois modules, structure of recurrence sequences, arithmetic of function field, and more recently dynamical systems and noise-induced order.

## Contents

# Computer Chess

Interested in computer chess and programming, Maurizio Monge developed his chess engines RattateChess and RattatAjedrez ^{[3]}.
He has further created various chess piece sets using Inkscape, available as SVG source, processed PNG files and XBoard theme ^{[4]}.

# Perfect Hashing

Motivated by the application of magic bitboards, Maurizio worked on its generalization of perfect hashing of numbers with sparse digit representation via multiplication by a constant, elaborating on Convolution, Toeplitz matrix, and Schur polynomial, published in 2010 on arXiv ^{[5]}, amd in 2011 in Discrete Applied Mathematics, Vol. 159, No. 11.

# Selected Publications

^{[6]} ^{[7]}

## 2009

- Maurizio Monge (
**2009**).*Generation of the Symmetric Field by Newton Polynomials in prime Characteristic*. arXiv:0903.3192 - Nevio Dubbini, Maurizio Monge (
**2009**).*An equivalent of Kronecker's Theorem for powers of an Algebraic Number and Structure of Linear Recurrences of fixed length*. arXiv:0910.5182 - Nevio Dubbini, Maurizio Monge, Antonio Bicchi (
**2009**).*Left invertibility of I/O quantized linear systems in dimension 1: a number theoretic approach*. arXiv:0911.0768

## 2010 ...

- Maurizio Monge (
**2010**).*Determination of the number of isomorphism classes of extensions of a p-adic field*. Journal of Number Theory, Vol. 131, No. 8^{[8]}^{[9]} - Giovanni Viglietta, Maurizio Monge (
**2010**).*The 3-dimensional searchlight scheduling problem*. CCCG 2010, pdf - Maurizio Monge (
**2010**).*On perfect hashing of numbers with sparse digit representation via multiplication by a constant*. arXiv:1003.3196 » Magic Bitboards - Maurizio Monge (
**2010**).*Determination of the number of isomorphism classes of extensions of a p-adic field*. arXiv:1011.0357 - Maurizio Monge (
**2011**).*On perfect hashing of numbers with sparse digit representation via multiplication by a constant*. Discrete Applied Mathematics, Vol. 159, No. 11 - Alessandro Cobbe, Maurizio Monge (
**2011**).*Answer to a question on A-groups, arisen from the study of Steinitz classes*. arXiv:1109.2065^{[10]} - Maurizio Monge (
**2011**).*A characterization of Eisenstein polynomials generating cyclic extensions of degree p2 and p3 over an unramified p-adic field*. arXiv:1109.4616^{[11]} - Maurizio Monge (
**2011**).*A family of Eisenstein polynomials generating totally ramified extensions, identification of extensions and construction of class fields*. arXiv:1109.4617 - Maurizio Monge (
**2012**).*A constructive theory for extensions of p-adic fields*. Ph.D. thesis, Scuola Normale Superiore di Pisa, advisor Roberto Dvornicich

## 2015 ...

- Jose F. Alves, Maurizio Monge (
**2015**).*Non-denseness of hyperbolicity for linear isomorphisms in Banach spaces*. arXiv:1510.05831^{[12]} - Ilaria Del Corso, Roberto Dvornicich, Maurizio Monge (
**2016**).*On wild extensions of a p-adic field*. arXiv:1601.05939 - Stefano Galatolo, Maurizio Monge, Isaia Nisoli (
**2017**).*Existence of Noise Induced Order, a Computer Aided Proof*. arXiv:1702.07024^{[13]}

# Forum Posts

- What is Botvinnik-Markov extension? by Maurizio Monge, CCC, October 26, 2005 » Botvinnik-Markoff Extension
- Conspiracy Numbers Search by Maurizio Monge, CCC, November 11, 2005 » Conspiracy Number Search
- A. STEEN vs. FRUIT 2.2.1 {Posted at request of Graham Banks & M. Monge} by A. Steen, CCC, November 24, 2005 » Fruit

# External Links

- Maurizio Monge's homepage - Programs
- Maurizio Monge's homepage - Chess art » Pieces, 2D Graphics Board, XBoard

# References

- ↑ Maurizio Monge | LinkedIn
- ↑ Maurizio Monge (
**2012**).*A constructive theory for extensions of p-adic fields*. Ph.D. thesis, Scuola Normale Superiore di Pisa, advisor Roberto Dvornicich - ↑ RattatAjedrez
- ↑ Maurizio Monge's homepage - Chess art
- ↑ Maurizio Monge (
**2010**).*On perfect hashing of numbers with sparse digit representation via multiplication by a constant*. arXiv:1003.3196 - ↑ dblp: Maurizio Monge
- ↑ Maurizio Monge - Google Scholar Citations
- ↑ Isomorphism class from Wikipedia
- ↑ p-adic number from Wikipedia
- ↑ Dedekind domain from Wikipedia
- ↑ Eisenstein's criterion from Wikipedia
- ↑ Banach space from Wikipedia
- ↑ Noise-induced order from Wikipedia