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Sökning: AMNE:(NATURVETENSKAP Matematik Diskret matematik) > Mälardalens universitet

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  • Eriksson, Henrik, et al. (författare)
  • Conjugacy of Coxeter elements
  • 2009
  • Ingår i: The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 16:2, s. R4-
  • Tidskriftsartikel (refereegranskat)
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  • Hellström, Lars, 1974- (författare)
  • Critical Pairs in Network Rewriting
  • 2014
  • Ingår i: IWC 2014. ; , s. 9-13
  • Konferensbidrag (refereegranskat)abstract
    • This extended abstract breifly introduces rewriting of networks (directed acyclic graphs with the extra structure needed to serve as expressions for PROducts and Permutations categories) and describes the critical pairs aspects of this theory. The author's interest in these comes from wanting to do equational reasoning in algebraic theories (such as Hopf algebras) that mix ordinary operations with co-operations; networks then serve as a formalism for expressions.The main message is to point out two phenomena that arise in network rewriting. The first is that of non-convexity of rules, wherein the left hand side of a rule need not be syntactically similar to a symbol in any extension of the underlying signature. The second is one of critical pairs potentially arising where two redexes wrap around each other even when they do not intersect.
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  • Sjöstrand, Jonas (författare)
  • On the sign-imbalance of partition shapes
  • 2005
  • Ingår i: Journal of combinatorial theory. Series A (Print). - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 111:2, s. 190-203
  • Tidskriftsartikel (refereegranskat)abstract
    • Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2([n/2]). We present a stronger theorem with a purely combinatorial proof using the Robinson-Schensted correspondence and a new concept called chess tableaux. We also prove a sharpening of another conjecture by Stanley concerning weighted sums of squares of sign-imbalances. The proof is built on a remarkably simple relation between the sign of a permutation and the signs of its RS-corresponding tableaux.
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  • Sjöstrand, Jonas (författare)
  • The cover pebbling theorem
  • 2005
  • Ingår i: The Electronic Journal of Combinatorics. - : The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 12:1, s. N22-
  • Tidskriftsartikel (refereegranskat)abstract
    • For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a cover pebbling starting with all pebbles on one node is trivial to compute and it was conjectured that the maximum of these simple cover pebbling numbers is indeed the general cover pebbling number of the graph. That is, for any configuration of this size, there exists a cover pebbling. In this note, we prove a generalization of the conjecture. All previously published results about cover pebbling numbers for special graphs (trees, hypercubes et cetera) are direct consequences of this theorem. We also prove that the cover pebbling number of a product of two graphs equals the product of the cover pebbling numbers of the graphs.
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