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Welcome to NORCOM 2019, The Nordic Combinatorial Conferences are held every third year the venue and organisation. rotating among the Nordic countries At NORCOM mathematicians from the Nordic countries as. well as from other countries meet and interact in an informal relaxed atmosphere All fields of. mathematics related to combinatorics and discrete mathematics are welcome. About the Nordic Combinatorial Conferences, This is the 13th Nordic Combinatorial Conference Previous conferences have taken place in. Denmark Finland Iceland Norway and Sweden To see a list of all former conferences and learn. more see the NORCOM homepage http www nordiccombinatorics org. This year s organisers,Lars D vling Andersen Aalborg University. Peter Beelen Technical University of Denmark, Trygve Johnsen UiT The Arctic University of Norway. Bjarne Toft University of Southern Denmark,NORCOM steering committee.

Einar Steingr msson University of Strathclyde,Lars D vling Andersen Aalborg University. Patric sterg rd Aalto University,Petter Br nd n KTH Royal Institute of Technology. Trygve Johnsen UiT The Arctic University of Norway. Forthcoming conferences, The 14th NORCOM conference will take place in 2022 in Norway Stay updated at. http www nordiccombinatorics org future html,Plenary speakers in order of appearance. Jack Edmonds,Kathie Cameron Wilfrid Laurier University.

Peter Michaelsen Hvideb k Pastorat,Olav Geil Aalborg University. Speakers alphabetically by surname,J rgen Bang Jensen University of Southern Denmark. ngela Barbero Universidad de Valladolid and yvind Ytrehus Simula UiB. Ignacio Cascudo Pueyo Aalborg University,Carl Johan Casselgren Link ping University. Mikhail Ganzhinov Aalto University,Oliver W Gnilke Aalborg University. Jonas Granholm Link ping University,Jaron Skovsted Gundersen Aalborg University.

Daniel Heinlein Aalto University,Anders Nedergaard Jensen Aarhus University. Trygve Johnsen UiT The Arctic University of Norway. Leif Kj r J rgensen Aalborg University,Dani Kotlar Tel Hai College. William Paavola Aalto University,Liam Solus KTH Royal Institute of Technology. Bjarne Toft Southern University of Denmark,Anders Yeo University of Southern Denmark. Patric sterg rd Aalto University,Participants alphabetically by surname.

Lars D vling Andersen Aalborg University lda math aau dk. J rgen Bang Jensen University of Southern Denmark jbj imada sdu dk. ngela Barbero Universidad de Valladolid angbar wmatem eis uva es. Thomas Bellitto University of Southern Denmark bellitto imada sdu dk. Kathie Cameron Wilfried Laurier University kcameron wlu ca. Ignacio Cascudo Pueyo Aalborg University ignacio math aau dk. Carl Johan Casselgren Link ping University carl johan casselgren liu se. Ren B dker Christensen Aalborg University rene math aau dk. Peter Danziger Ryerson University Danziger ryerson ca. Jack Edmonds jack n2m2m6 gmail com, Enrique Garcia Moreno Esteva University of Helsinki egarcia math cinvestav edu mx. Mikhail Ganzhinov Aalto University mikhail ganzhinov aalto fi. Olav Geil Aalborg University olav math aau dk, Oliver W Gnilke Aalborg University owg math aau dk. Jonas Granholm Link ping University jonas granholm liu se. Jaron Skovsted Gundersen Aalborg University jaron math aau dk. Daniel Heinlein Aalto University daniel heinlein aalto fi. Anders Nedergaard Jensen Aarhus University Jensen math au dk. Tommy Jensen tommyrjensen gmail com, Katharina Jochemko KTH Royal Institute of Technology jochemko kth se. Trygve Johnsen UiT The Arctic University of Norway Trygve Johnsen uit no. Leif Kj r J rgensen Aalborg University leif math aau dk. Dani Kotlar Tel Hai College dannykotlar gmail com, Peter Michaelsen Hvideb k Pastorat PMI KM DK part of the conference. William Paavola Aalto University william paavola aalto fi. Samu Potka KTH Royal Institute of Technology potka kth se. Liam Solus KTH Royal Institute of Technology solus kth se. Carsten Thomassen Technical University of Denmark ctho dtu dk part of the conference. Bjarne Toft Southern University of Denmark btoft imada sdu dk. Christian Wulff Nielsen University of Copenhagen koolooz di ku dk. Anders Yeo University of Southern Denmark yeo imada sdu dk. yvind Ytrehus Simula UiB oyvindy simula no, Patric sterg rd Aalto University patric ostergard aalto fi.

Monday August 5,12 00 13 00 Lunch, 13 00 13 30 Welcome and introduction to Sch fferg rden by a representative from the. Foundation for Danish Norwegian Cooperation which owns Sch fferg rden and has supported. the conference considerably, 13 30 14 30 Jack Edmonds Origins of NP and P The full story NP P. 14 30 15 00 Coffee and tea, 15 00 17 30 Contributed talks chair Trygve Johnsen. Anders Yeo Spanning eulerian subdigraphs avoiding k prescribed arcs in tournaments. Carl Johan Casselgren Latin squares and Latin cubes with forbidden entries. Dani Kotlar On sequential basis replacement in matroids. Leif Kj r J rgensen Automorphisms of an srg 162 21 0 3. Patric sterg rd r sparse Steiner Triple Systems,18 00 Dinner. Tuesday August 6,8 00 9 00 Breakfast, 9 00 10 00 Kathie Cameron Parity theorems about trees and cycles.

10 00 10 30 Coffee and tea, 10 30 12 00 Contributed talks chair Carl Johan Casselgren. Jonas Granholm A localization method in Hamiltonian graph theory. J rgen Bang Jensen Good acyclic orientations antistrong digraphs and matroids. Mikhail Ganzhinov Construction of biangular line sets in low dimensional Euclidian. 12 00 13 00 Lunch, 13 00 13 30 Peter Michaelsen The Nordic running fight games Dald s and. 13 30 15 00 Contributed talks chair Bjarne Toft,Bjarne Toft Hex the full story. Ignacio Cascudo Pueyo Squares of cyclic codes,Oliver W Gnilke Symmetric mosaics. 15 00 15 30 Coffee and tea, 15 30 17 30 Contributed talks chair Leif Kj r J rgensen.

Daniel Heinlein Degree tables, Jaron Skovsted Gundersen Improved bounds on the threshold gap in ramp secret sharing. Liam Solus Real zeros and the alternatingly increasing property in algebraic. combinatorics, William Paavola Quaternary complex Hadamard matrices of order 18. 18 00 Conference dinner,Wednesday August 7,8 00 9 00 Breakfast. 9 00 10 00 Olav Geil Bounding the number of affine roots with applications in. communication theory,10 00 10 30 Coffee and tea, 10 30 12 00 Contributed talks chair Patric sterg rd. Anders Nedergaard Jensen Tropical homotopy continuation. ngela Barbero yvind Ytrehus Bounds for convolutional codes. Trygve Johnsen Generalized weights of rank metric codes a combinatorial approach. 12 00 Closing and lunch,Abstracts main speakers in order of appearance.

Origins of NP and P The Full Story NP P,Jack Edmonds. Inspired by the new book Hex The Full Story I present an account beginning for me in 1960. of NP coNP and the conjecture NP P Prompted by the Konig Egervary polyhedral theory of. 1931 for the optimum assignment problem the Baruvka algorithm of 1926 for minimum spanning. trees and the Dantzig Fulkerson Johnson polyhedral algorithm of 1954 for the TSP I spent several. years trying to find a polynomial time algorithm for TSP. Failing that I conjectured NP P in 1966 While looking I did find polynomial time polyhedral. algorithms for some other problems including OBS Given a digraph G specified root nodes r i. and a cost for each edge of G find a least cost collectionof edge disjoint directed spanning trees in. G rooted respectively at the nodes r i i e r i branchings in G. The extensively treated min cost network flow problem is a special case of OBS However OBS. does not reduce to it Curiously the simplest way which I know to describe a good. algorithm for OBS is by matroid intersection for general matroids. Prompted by Julius Petersen s theorem of 1891 I did find a polynomial time algorithm for. finding in a graph G with weighted edges a min cost total weight spanning degree 2 subgraph G. of G However G is perhaps not connected, This talk is related to talks given in Lisbon on Feb 20 T cnico Lisboa and at the Sorbonne in. Paris on May 3 and at a Celebration of the work of Stephen Cook in 50 Years of Computational. Complexity Fields Institute Toronto on May 9 2019 God provides only a few glimpses of. Monday 13 30,Tuesday 9 00,The Nordic running fight games Dald s and S hkku. Peter Michaelsen Hvideb k Pastorat, In his book De Ludis Orientalibus Oxford 1694 the English orientalist Thomas Hyde 1636 1703. devoted a chapter Historia Tabiludii to a category of board games which was popular among. Arabs Turks and Persians in the Middle East at that time One of these games t b has been. played in Egypt since at least the 13th c A D, Following Hyde T b games along with running fight games has been used to designate this.

class of games which essentially combines the methods of race games like backgammon and. ludo and the goal of elimination based war games such as draughts Like in race games pieces. are moved along linear tracks based on the cast of dice or other lots but like in draughts the. object is to capture opponent s pieces, This family of dice board games has or had members in a lot of countries including Greece large. parts of Africa India the Comoros Isles and even as far away as among the Nivkh people in. Eastern Siberia, In this lecture I will give a short presentation of the two Scandinavian members of the T b or. running fight family the Danish Norwegian dald s a and the S mi s hkku and discuss the. interesting question how these originally Arab games might have spread to Northern Europe. My first article on Dald s and S hkku was published in the Danish journal Ord Sag 20 years ago. Two years later a large part of the journal Board Games Studies issue 4 was devoted to articles. about these and other running fight games written by several researchers Since then a lot of. new information has been discovered and in 2012 I tried to make a survey of the situation in my. article Un Jeu M dieval Arabe en Scandinavie in the magazine Histoire et Images Medievales. During the last few years archeologists have found several new traces of this type of games. around in Europe Besides the almost extinct S hkku game has experienced a renaissance in many. places in Norway Northern Sweden and Northern Finland thanks to the efforts of S mi board. game enthusiasts in Norway They have already contributed with important new information. about the rules history and geographical distribution of S hkku and other traditional S mi games. and will undoubtedly continue to do so in the future. Tuesday 13 00,Wednesday 9 00, Abstracts other speakers alphabetically by surname. Tuesday 11 00,Bounds for convolutional codes, ngela Barbero Universidad de Valladolid and yvind Ytrehus Simula UiB. A q ary error correcting convolutional code is determined by a linear encoder by which an n bit. output vector is produced as a linear combination of the current k bit input vector and one or. more previous input vectors Convolutional codes are attractive in many cases because they offer. a better application dependent tradeoff between block size n code rate k n decoding complexity. and or decoding delay than corresponding q ary block codes with error correction performance. As for block codes it is desirable to find the best convolutional code given q n and k While the. problem of deriving bounds for block codes is a mature area less is known about finding tight. lower and upper bounds for convolutional codes We will describe upper and lower bounds for. convolutional codes,Wednesday 11 00,Squares of cyclic codes.

Ignacio Cascudo Pueyo Aalborg Unversity, The square of a linear code C is the code spanned over the same finite field by the. set of componentwise products of every pair of non necessarily distinct codewords. from C This notion is interesting because of certain applications in particular in the. area of secure multiparty computation within cryptography where it is interesting. to find codes with large rate whose squares have large minimum distance I will. explain some of my recent results where I construct cyclic codes with such. characteristics which in turn motivates a problem on finding large sets of integers. with certain properties and counting their cardinalities. Tuesday 14 00,Monday 15 30, Construction of biangular line sets in low dimensional Euclidian spaces. Mikhail Ganzhinov Aalto University, A set of lines in Euclidean space is called biangular if the angle between each pair of lines can have. only two values In this computer aided work we use combined approach of isomorph free. exhaustive generation of candidate Gram matrices with indeterminate angles and Gr bner basis. computation to classify the largest biangular sets of lines Classification up to dimension 6 is. obtained This is joined work with Ferenc S ll si,Tuesday 11 30. 13TH NORDIC COMBINATORIAL CONFERENCE Sch fferg rden Copenhagen Denmark August 5 7 2019 https norcom2019 math aau dk We would like to acknowledge support from following sponsors Welcome to NORCOM 2019 The Nordic Combinatorial Conferences are held every third year the venue and organisation rotating among the Nordic countries At NORCOM mathematicians from the Nordic

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