{"results":[{"id":"crossref_10.1016/j.scriptamat.2022.114941","title":"Improved dynamic strength of TRIP steel via pre-straining","authors":[{"name":"JT Lloyd"},{"name":"DJ Magagnosc"},{"name":"CS Meredith"},{"name":"KR Limmer"},{"name":"DM Field"}],"abstract":"","source":"CrossRef","year":2022,"language":"en","subjects":null,"doi":"10.1016/j.scriptamat.2022.114941","url":"https://doi.org/10.1016/j.scriptamat.2022.114941","is_open_access":true,"citations":13,"published_at":"","score":66.39},{"id":"doaj_10.46298/dmtcs.2500","title":"The $(m, n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q, t$-symmetry","authors":[{"name":"Ryan Kaliszewski"},{"name":"Huilan Li"}],"abstract":"We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area; skip; dinv) are given, we have an algorithm to construct the marked rank word corresponding to the triple. By considering all valid triples we give an explicit formula for the $(m,n)$-rational $q; t$-Catalan polynomials when $m=3$. Then there is a natural bijection on the triples of statistics (area; skip; dinv) which exchanges the statistics area and dinv while fixing the skip. Thus we prove the $q; t$-symmetry of $(m,n)$-rational $q; t$-Catalan polynomials for $m=3$..","source":"DOAJ","year":2015,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2500","url":"https://dmtcs.episciences.org/2500/pdf","pdf_url":"https://dmtcs.episciences.org/2500/pdf","is_open_access":true,"published_at":"","score":59},{"id":"doaj_10.46298/dmtcs.2528","title":"Statistics on Lattice Walks and q-Lassalle Numbers","authors":[{"name":"Lenny Tevlin"}],"abstract":"This paper contains two results. First, I propose a $q$-generalization of a certain sequence of positive integers, related to Catalan numbers, introduced by Zeilberger, see Lassalle (2010). These $q$-integers are palindromic polynomials in $q$ with positive integer coefficients. The positivity depends on the positivity of a certain difference of products of $q$-binomial coefficients.To this end, I introduce a new inversion/major statistics on lattice walks. The difference in $q$-binomial coefficients is then seen as a generating function of weighted walks that remain in the upper half-plan.","source":"DOAJ","year":2015,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2528","url":"https://dmtcs.episciences.org/2528/pdf","pdf_url":"https://dmtcs.episciences.org/2528/pdf","is_open_access":true,"published_at":"","score":59},{"id":"ss_d260013ae128bdf26bb18fc6e79f02933a069c76","title":"3-extra Connectivity of 3-ary N-cube Networks","authors":[{"name":"Mei-Mei Gu"},{"name":"Rongxia Hao"}],"abstract":"Let G be a connected graph and S be a set of vertices. The h-extra connectivity of G is the cardinality of a minimum set S such that G-S is disconnected and each component of G-S has at least h+1 vertices. The h-extra connectivity is an important parameter to measure the reliability and fault tolerance ability of large interconnection networks. The h-extra connectivity for h=1,2 of k-ary n-cube are gotten by Hsieh et al. in [Theoretical Computer Science, 443 (2012) 63-69] for k\u003e=4 and Zhu et al. in [Theory of Computing Systems, arxiv.org/pdf/1105.0991v1 [cs.DM] 5 May 2011] for k=3. In this paper, we show that the h-extra connectivity of the 3-ary n-cube networks for h=3 is equal to 8n-12, where n\u003e=3.","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Computer Science","Mathematics"],"doi":"10.1016/j.ipl.2014.04.003","url":"https://www.semanticscholar.org/paper/d260013ae128bdf26bb18fc6e79f02933a069c76","pdf_url":"http://arxiv.org/pdf/1309.5083.pdf","is_open_access":true,"citations":56,"published_at":"","score":58.68},{"id":"doaj_10.46298/dmtcs.2449","title":"Chevalley-Monk and Giambelli formulas for Peterson Varieties","authors":[{"name":"Elizabeth Drellich"}],"abstract":"A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli's formula for all Lie types.","source":"DOAJ","year":2014,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2449","url":"https://dmtcs.episciences.org/2449/pdf","pdf_url":"https://dmtcs.episciences.org/2449/pdf","is_open_access":true,"published_at":"","score":58},{"id":"doaj_10.46298/dmtcs.2089","title":"Determining pure discrete spectrum for some self-affine tilings","authors":[{"name":"Shigeki Akiyama"},{"name":"Franz Gähler"},{"name":"Jeong-Yup Lee"}],"abstract":"Discrete Algorithms","source":"DOAJ","year":2014,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2089","url":"https://dmtcs.episciences.org/2089/pdf","pdf_url":"https://dmtcs.episciences.org/2089/pdf","is_open_access":true,"published_at":"","score":58},{"id":"ss_aeff51ed947488ff20188d8e3c448a045c7524c6","title":"Avoiding 5-Circuits in 2-Factors of Cubic Graphs","authors":[{"name":"Barbora Candráková"},{"name":"Robert Lukoťka"}],"abstract":"We show that every bridgeless cubic graph $G$ on $n$ vertices other than the Petersen graph has a 2-factor with at most $2(n-2)/15$ circuits of length $5$. An infinite family of graphs attains this bound. We also show that $G$ has a 2-factor with at most $n/5.8\\overline{3}$ odd circuits. This improves the previously known bound of $n/5.41$ [Luko\\v{t}ka, M\\'a\\v{c}ajov\\'a, Maz\\'ak, \\v{S}koviera: Small snarks with large oddness, arXiv:1212.3641 [cs.DM] ].","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Mathematics","Computer Science"],"doi":"10.1137/130942966","url":"https://www.semanticscholar.org/paper/aeff51ed947488ff20188d8e3c448a045c7524c6","pdf_url":"http://arxiv.org/pdf/1311.0512","is_open_access":true,"citations":4,"published_at":"","score":57.12},{"id":"doaj_10.46298/dmtcs.12814","title":"Type $A$ molecules are Kazhdan-Lusztig","authors":[{"name":"Michael Chmutov"}],"abstract":"Let $(W, S)$ be a Coxeter system. A $W$-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the $W$-graph corresponding to the action of the Iwahori-Hecke algebra on the Kazhdan-Lusztig basis as well as this graph's strongly connected components (cells). In 2008, Stembridge identified some common features of the Kazhdan-Lusztig graphs (\"admissibility'') and gave combinatorial rules for detecting admissible $W$-graphs. He conjectured, and checked up to $n=9$, that all admissible $A_n$-cells are Kazhdan-Lusztig cells. The current paper provides a possible first step toward a proof of the conjecture. More concretely, we prove that the connected subgraphs of $A_n$-cells consisting of simple (i.e. directed both ways) edges do fit into the Kazhdan-Lusztig cells.","source":"DOAJ","year":2013,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.12814","url":"https://dmtcs.episciences.org/12814/pdf","pdf_url":"https://dmtcs.episciences.org/12814/pdf","is_open_access":true,"published_at":"","score":57},{"id":"doaj_10.46298/dmtcs.2331","title":"Generalized monotone triangles","authors":[{"name":"Lukas Riegler"}],"abstract":"In a recent work, the combinatorial interpretation of the polynomial $\\alpha (n; k_1,k_2,\\ldots,k_n)$ counting the number of Monotone Triangles with bottom row $k_1 \u003c k_2 \u003c ⋯\u003c k_n$ was extended to weakly decreasing sequences $k_1 ≥k_2 ≥⋯≥k_n$. In this case the evaluation of the polynomial is equal to a signed enumeration of objects called Decreasing Monotone Triangles. In this paper we define Generalized Monotone Triangles – a joint generalization of both ordinary Monotone Triangles and Decreasing Monotone Triangles. As main result of the paper we prove that the evaluation of $\\alpha (n; k_1,k_2,\\ldots,k_n)$ at arbitrary $(k_1,k_2,\\ldots,k_n) ∈ \\mathbb{Z}^n$ is a signed enumeration of Generalized Monotone Triangles with bottom row $(k_1,k_2,\\ldots,k_n)$. Computational experiments indicate that certain evaluations of the polynomial at integral sequences yield well-known round numbers related to Alternating Sign Matrices. The main result provides a combinatorial interpretation of the conjectured identities and could turn out useful in giving bijective proofs.","source":"DOAJ","year":2013,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2331","url":"https://dmtcs.episciences.org/2331/pdf","pdf_url":"https://dmtcs.episciences.org/2331/pdf","is_open_access":true,"published_at":"","score":57},{"id":"doaj_10.46298/dmtcs.2336","title":"Gale-Robinson Sequences and Brane Tilings","authors":[{"name":"In-Jee Jeong"},{"name":"Gregg Musiker"},{"name":"Sicong Zhang"}],"abstract":"We study variants of Gale-Robinson sequences, as motivated by cluster algebras with principal coefficients. For such cases, we give combinatorial interpretations of cluster variables using brane tilings, as from the physics literature.","source":"DOAJ","year":2013,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2336","url":"https://dmtcs.episciences.org/2336/pdf","pdf_url":"https://dmtcs.episciences.org/2336/pdf","is_open_access":true,"published_at":"","score":57},{"id":"doaj_10.46298/dmtcs.2342","title":"Balanced labellings of affine permutations","authors":[{"name":"Hwanchul Yoo"},{"name":"Taedong Yun"}],"abstract":"We study the $\\textit{diagrams}$ of affine permutations and their $\\textit{balanced}$ labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, we show that the sum of weight monomials of the $\\textit{column strict}$ balanced labellings is the affine Stanley symmetric function defined by Lam and we give a simple algorithm to recover reduced words from balanced labellings. Applying this theory, we give a necessary and sufficient condition for a diagram to be an affine permutation diagram. Finally, we conjecture that if two affine permutations are $\\textit{diagram equivalent}$ then their affine Stanley symmetric functions coincide.","source":"DOAJ","year":2013,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2342","url":"https://dmtcs.episciences.org/2342/pdf","pdf_url":"https://dmtcs.episciences.org/2342/pdf","is_open_access":true,"published_at":"","score":57},{"id":"doaj_10.46298/dmtcs.586","title":"On paths, trails and closed trails in edge-colored graphs","authors":[{"name":"Laurent Gourvès"},{"name":"Adria Lyra"},{"name":"Carlos A. Martinhon"},{"name":"Jérôme Monnot"}],"abstract":"Graph Theory","source":"DOAJ","year":2012,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.586","url":"https://dmtcs.episciences.org/586/pdf","pdf_url":"https://dmtcs.episciences.org/586/pdf","is_open_access":true,"published_at":"","score":56},{"id":"doaj_10.46298/dmtcs.2943","title":"Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract)","authors":[{"name":"Pierre-Loïc Méliot"}],"abstract":"We show that the shapes of integer partitions chosen randomly according to Schur-Weyl measures of parameter $\\alpha =1/2$ and Gelfand measures satisfy Kerov's central limit theorem. Thus, there is a gaussian process $\\Delta$ such that under Plancherel, Schur-Weyl or Gelfand measures, the deviations $\\Delta_n(s)=\\lambda _n(\\sqrt{n} s)-\\sqrt{n} \\lambda _{\\infty}^{\\ast}(s)$ converge in law towards $\\Delta (s)$, up to a translation along the $x$-axis in the case of Schur-Weyl measures, and up to a factor $\\sqrt{2}$ and a deterministic remainder in the case of Gelfand measures. The proofs of these results follow the one given by Ivanov and Olshanski for Plancherel measures; hence, one uses a \"method of noncommutative moments''.","source":"DOAJ","year":2011,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2943","url":"https://dmtcs.episciences.org/2943/pdf","pdf_url":"https://dmtcs.episciences.org/2943/pdf","is_open_access":true,"published_at":"","score":55},{"id":"doaj_10.46298/dmtcs.514","title":"Synchronizing random automata","authors":[{"name":"Evgeny Skvortsov"},{"name":"Yulia Zaks"}],"abstract":"special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications","source":"DOAJ","year":2010,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.514","url":"https://dmtcs.episciences.org/514/pdf","pdf_url":"https://dmtcs.episciences.org/514/pdf","is_open_access":true,"published_at":"","score":54},{"id":"doaj_10.46298/dmtcs.498","title":"Asymptotic variance of random symmetric digital search trees","authors":[{"name":"Hsien-Kuei Hwang"},{"name":"Michael Fuchs"},{"name":"Vytas Zacharovas"}],"abstract":"Dedicated to the 60th birthday of Philippe Flajolet","source":"DOAJ","year":2010,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.498","url":"https://dmtcs.episciences.org/498/pdf","pdf_url":"https://dmtcs.episciences.org/498/pdf","is_open_access":true,"published_at":"","score":54},{"id":"doaj_10.46298/dmtcs.2683","title":"Another bijection between $2$-triangulations and pairs of non-crossing Dyck paths","authors":[{"name":"Carlos M. Nicolás"}],"abstract":"A $k$-triangulation of the $n$-gon is a maximal set of diagonals of the $n$-gon containing no subset of $k+1$ mutually crossing diagonals. The number of $k$-triangulations of the $n$-gon, determined by Jakob Jonsson, is equal to a $k \\times k$ Hankel determinant of Catalan numbers. This determinant is also equal to the number of $k$ non-crossing Dyck paths of semi-length $n-2k$. This brings up the problem of finding a combinatorial bijection between these two sets. In FPSAC 2007, Elizalde presented such a bijection for the case $k=2$. We construct another bijection for this case that is stronger and simpler that Elizalde's. The bijection preserves two sets of parameters, degrees and generalized returns. As a corollary, we generalize Jonsson's formula for $k=2$ by counting the number of $2$-triangulations of the $n$-gon with a given degree at a fixed vertex.","source":"DOAJ","year":2009,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2683","url":"https://dmtcs.episciences.org/2683/pdf","pdf_url":"https://dmtcs.episciences.org/2683/pdf","is_open_access":true,"published_at":"","score":53},{"id":"doaj_10.46298/dmtcs.2694","title":"On the 2-adic order of Stirling numbers of the second kind and their differences","authors":[{"name":"Tamás Lengyel"}],"abstract":"Let $n$ and $k$ be positive integers, $d(k)$ and $\\nu_2(k)$ denote the number of ones in the binary representation of $k$ and the highest power of two dividing $k$, respectively. De Wannemacker recently proved for the Stirling numbers of the second kind that $\\nu_2(S(2^n,k))=d(k)-1, 1\\leq k \\leq 2^n$. Here we prove that $\\nu_2(S(c2^n,k))=d(k)-1, 1\\leq k \\leq 2^n$, for any positive integer $c$. We improve and extend this statement in some special cases. For the difference, we obtain lower bounds on $\\nu_2(S(c2^{n+1}+u,k)-S(c2^n+u,k))$ for any nonnegative integer $u$, make a conjecture on the exact order and, for $u=0$, prove part of it when $k \\leq 6$, or $k \\geq 5$ and $d(k) \\leq 2$. The proofs rely on congruential identities for power series and polynomials related to the Stirling numbers and Bell polynomials, and some divisibility properties.","source":"DOAJ","year":2009,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2694","url":"https://dmtcs.episciences.org/2694/pdf","pdf_url":"https://dmtcs.episciences.org/2694/pdf","is_open_access":true,"published_at":"","score":53},{"id":"doaj_10.46298/dmtcs.3647","title":"Enumeration of orientable coverings of a non-orientable manifold","authors":[{"name":"Jin Ho Kwak"},{"name":"Alexander Mednykh"},{"name":"Roman Nedela"}],"abstract":"In this paper we solve the known V.A. Liskovets problem (1996) on the enumeration of orientable coverings over a non-orientable manifold with an arbitrary finitely generated fundamental group. As an application we obtain general formulas for the number of chiral and reflexible coverings over the manifold. As a further application, we count the chiral and reflexible maps and hypermaps on a closed orientable surface by the number of edges. Also, by this method the number of self-dual and Petri-dual maps can be determined. This will be done in forthcoming papers by authors.","source":"DOAJ","year":2008,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3647","url":"https://dmtcs.episciences.org/3647/pdf","pdf_url":"https://dmtcs.episciences.org/3647/pdf","is_open_access":true,"published_at":"","score":52},{"id":"doaj_10.46298/dmtcs.432","title":"Counting descents, rises, and levels, with prescribed first element, in words","authors":[{"name":"Sergey Kitaev"},{"name":"Toufik Mansour"},{"name":"Jeff Remmel"}],"abstract":"Combinatorics","source":"DOAJ","year":2008,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.432","url":"https://dmtcs.episciences.org/432/pdf","pdf_url":"https://dmtcs.episciences.org/432/pdf","is_open_access":true,"published_at":"","score":52},{"id":"doaj_10.46298/dmtcs.408","title":"Exponential bounds and tails for additive random recursive sequences","authors":[{"name":"Ludger Rüschendorf"},{"name":"Eva-Maria Schopp"}],"abstract":"Analysis of Algorithms","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.408","url":"https://dmtcs.episciences.org/408/pdf","pdf_url":"https://dmtcs.episciences.org/408/pdf","is_open_access":true,"published_at":"","score":51}],"total":151623,"page":1,"page_size":20,"sources":["DOAJ","Semantic Scholar","CrossRef"],"query":"cs.DM"}