Izbrane bodo nekatere standardne teme iz podiplomske diskretne matematike. Možne teme so na primer: simetrije grafov, diskretna geometrija, algebraična in topološka teorija grafov, konfiguracije, ekstremalni grafi, uporaba grafov v znanosti in tehniki, simetrične funkcije, kombinatorične zvrsti, naprednejše metode kombinatoričnega preštevanja.
Izbira je lahko odvisna od interesov in raziskovalne usmeritve študentov.
Izbrana poglavja iz diskretne matematike
2019/2020
Program:
Doktorski študijski program 3. stopnje Matematika in fizika
Smer:
Matematika
Letnik:
1 ali 2 letnik
Semester:
prvi ali drugi
Vrsta:
izbirni
ECTS:
6
Jezik:
slovenski, angleški
Nosilec predmeta:
prof. dr. Sandi Klavžar, prof. dr. Matjaž Konvalinka, prof. dr. Marko Petkovšek, prof. dr. Riste Škrekovski
Izvajalec (kontaktna oseba):
Ure na teden – 1. ali 2. semester:
Predavanja
2
Seminar
0
Vaje
0
Laboratorij
0
Vsebina
Temeljni literatura in viri
Richard P. Stanley: Enumerative Combinatorics, Vol. 1 and 2, Cambridge University Press, New York-Cambridge, 1999, 2011.
R. Diestel: Graph Theory, 3rd ed., Springer, 2005.
J. A. Bondy, U. S. R. Murty: Graph Theory with Applications, 2nd ed., Springer, 2008.
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Oxford, University Press, 1995
Cilji in kompetence
Namen predmeta je seznaniti študente z nekaterimi pomembnimi temami diskretne matematike.
Predvideni študijski rezultati
Znanje in razumevanje predstavljenih konceptov.
Sposobnost uporabe pridobljenega znanja in spretnosti.
Metode poučevanja in učenja
Predavanja, konzultacije, reševanje problemov
Načini ocenjevanja
Pisni izpit (domače naloge), ustni izpit.
(ocene: 5 (negativno), 6-10 (pozitivno), ob upoštevanju Statuta UL)
Reference nosilca
Sandi Klavžar:
DORBEC, Paul, KLAVŽAR, Sandi. Generalized power domination: propagation radius and Sierpiński graphs. Acta applicandae mathematicae, ISSN 0167-8019, 2014, vol. 134, iss. 1, str. 75-86. [COBISS-SI-ID 17148249]
KLAVŽAR, Sandi. Structure of Fibonacci cubes: a survey. Journal of combinatorial optimization, ISSN 1382-6905, 2013, vol. 25, iss. 4, str. 505-522. [COBISS-SI-ID 16603737]
HAMMACK, Richard H., IMRICH, Wilfried, KLAVŽAR, Sandi. Handbook of product graphs, (Discrete mathematics and its applications). Boca Raton London New York: CRC Press, cop. 2011. XVIII, 518 str., ilustr. ISBN 978-1-4398-1304-1. [COBISS-SI-ID 15916121]
Matjaž Konvalinka:
KONVALINKA, Matjaž, PAK, Igor. Triangulations of Cayley and Tutte polytopes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 245, str. 1-33. [COBISS-SI-ID 16706905]
KONVALINKA, Matjaž. Skew quantum Murnaghan-Nakayama rule. Journal of algebraic combinatorics, ISSN 0925-9899, 2012, vol. 35, no. 4, str. 519-545. [COBISS-SI-ID 16250713]
KONVALINKA, Matjaž. Divisibility of generalized Catalan numbers. Journal of combinatorial theory. Series A, ISSN 0097-3165, 2007, vol. 114, iss. 6, str. 1089-1100. [COBISS-SI-ID 14354265]
Marko Petkovšek:
ABRAMOV, Sergei A., BARKATOU, Moulay A., VAN HOEIJ, Mark, PETKOVŠEK, Marko. Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences. Journal of symbolic computation, ISSN 0747-7171, 2011, vol. 46, iss. 11, str. 1205-1228. [COBISS-SI-ID 16083033]
BRESSLER, Andrew, GREENWOOD, Torin, PEMANTLE, Robin, PETKOVŠEK, Marko. Quantum random walk on the integer lattice: examples and phenomena. V: AMS Special Sessions on Algorithmic Probability and Combinatorics, October 5-6, 2007, DePaul University, Chicago (Illinois), October 4-5, 2008, University of British Columbia, Vancouver (BC, Canada). LLADSER, Manuel (ur.), et al. Algorithmic probability and combinatorics : AMS special sessions on algorithmic probability and combinatorics, October 5-6, 2007, DePaul University, Chicago, Illinois, October 4-5, 2008, University of British Columbia, Vancouver, BC, Canada, (Contemporary mathematics, ISSN 0271-4132, 520). Providence: American Mathematical Society, cop. 2010, str. 41-60. [COBISS-SI-ID 15813977]
KLAVŽAR, Sandi, MOLLARD, Michel, PETKOVŠEK, Marko. The degree sequence of Fibonacci and Lucas cubes. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2011, vol. 311, iss. 14, str. 1310-1322. [COBISS-SI-ID 15884121]
Riste Škrekovski:
KNOR, Martin, LUŽAR, Borut, ŠKREKOVSKI, Riste. Sandwiching the (generalized) Randić index. Discrete applied mathematics, ISSN 0166-218X. [Print ed.], 2015, vol. 181, str. 160-166. [COBISS-SI-ID 2048330515]
KAISER, Tomáš, STEHLÍK, Matěj, ŠKREKOVSKI, Riste. Replication in critical graphs and the persistence of monomial ideals. Journal of combinatorial theory. Series A, ISSN 0097-3165, 2014, vol. 123, iss. 1, str. 239-251. [COBISS-SI-ID 16920665]
VUKAŠINOVIĆ, Vida, GREGOR, Petr, ŠKREKOVSKI, Riste. On the mutually independent Hamiltonian cycles in faulty hypercubes. Information sciences, ISSN 0020-0255. [Print ed.], jul. 2013, vol. 236, str. 224-235. [COBISS-SI-ID 26622247]
