Results 51 to 60 of about 3,063 (228)
Patterns in matchings and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs.
Jonathan Bloom, Sergi Elizalde
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Topology and its Applications, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Journal of Combinatorial Theory, Series A, 1981 AbstractIn this paper we give a bijection between the partitions of n with parts congruent to 1 or 4 (mod 5) and the partitions of n with parts differing by at least 2. This bijection is obtained by a cut-and-paste procedure which starts with a partition in one class and ends with a partition in the other class.
Stephen C. Milne, Adriano M. Garsia
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A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions
Forum of Mathematics, SigmaWe characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams.
Daoji Huang, Jessica Striker
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A Bijection for Tricellular Maps
ISRN Discrete Mathematics, 2013 We give a bijective proof for a relation between unicellular, bicellular, and tricellular maps. These maps represent cell complexes of orientable surfaces having one, two, or three boundary components. The relation can formally be obtained using matrix theory (Dyson, 1949) employing the Schwinger-Dyson equation (Schwinger, 1951).
Han, Hillary Siwei, Reidys, Christian
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A combinatorial interpretation of the bijection of Goulden and Yong
AKCE International Journal of Graphs and Combinatorics, 2020 We define a dual of a graph, generalizing the definition of Goulden et al. (2002), which only applies to trees; then we reprove their main result using our new definition.
Kerry Ojakian
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Statistics on staircase tableaux, eulerian and mahonian statistics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a simple bijection between some staircase tableaux and tables of inversion. Some nice properties of the bijection allows us to define some q-Eulerian polynomials related to the staircase tableaux.
Sylvie Corteel, Sandrine Dasse-Hartaut
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A simple model of trees for unicellular maps [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We consider unicellular maps, or polygon gluings, of fixed genus. In FPSAC '09 the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for these objects.
Guillaume Chapuy +2 more
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Steiner Triple Systems With High Discrepancy
Journal of Combinatorial Designs, EarlyView.ABSTRACT In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed r ≥ 3 $r\ge 3$ and n ≡ 1 , 3 ( mod 6 ) $n\equiv 1,3\,(\mathrm{mod}\,6)$, any r $r$‐colouring of the triples on [ n ] $[n]$ admits a Steiner triple system of order n $n$ with discrepancy Ω ( n 2 ) ${\rm{\Omega }}({
Lior Gishboliner +2 more
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Rigged configurations of type $D_4^{(3)}$ and the filling map [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a statistic preserving bijection from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals $\otimes_{i=1}^{N}B^{1,s_i}$ in type $D_4^{(3)}$ by using virtualization into type $D_4^{(1)}$.
Travis Scrimshaw
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