Characterization of certain families of modular multiplicative divisor graphs by R. Revathi, S. Ganesh

“…Sethuraman in AKCE International Journal of Graphs and Combinatorics, No. 1 (2009) 229–236. In addition, we discuss the role of MMD labelling in obtaining cyclic decompositions of certain families of graphs into specific graphs.…”
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Triangle Decompositions of Planar Graphs by Mynhardt Christina M., Bommel Christopher M. van

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Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak by Green, B

“…This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer science. …”

Algebraic systems biology: a case study for the Wnt pathway by Gross, E, Harrington, H, Rosen, Z, Sturmfels, B

“…We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.…”

Parsimonious reconstruction of sequence evolution and haplotype blocks: Finding the minimum number of recombination events by Song, Y, Hein, J

“…Our approach is deterministic and is based on the combinatorics of leaf-labelled rooted trees. In contrast to previously known approaches, which only yield estimated lower bounds, our approach always gives the exact minimum number of recombination events. …”

Toric Hypersymplectic Quotients by Dancer, A, Swann, A

“…We give precise conditions for smoothness and non-degeneracy of such quotients and show how some properties of the quotient geometry and topology are constrained by the combinatorics of the cone configurations. Examples are studied, including non-trivial structures on R^{4n} and metrics on complements of hypersurfaces in compact manifolds.…”

T-structures on some local Calabi-Yau varieties by Bridgeland, T

“…We use the theory of exceptional collections to describe t-structures on the derived category of coherent sheaves on ωZ. The combinatorics of these t-structures is determined by a natural action of an affine braid group, closely related to the well-known action of the Artin braid group on the set of exceptional collections on Z. © 2005 Elsevier Inc. …”

The threshold for jigsaw percolation on random graphs by Bollobás, B, Riordan, O, Slivken, E, Smith, P

On the factor-thickness of regular graphs by Peng, Yee Hock, Chen, Chuan Chong, Koh, Khee Meng

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ADVANCED LINEAR ALGEBRA / by Loehr, Nicholas A., author. 650211, , author

“…The goal of this book is to explore a variety of advanced topics in linear algebra, which highlight the rich interconnections linking this subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. …”

Constrained ear decompositions in graphs and digraphs by Frédéric Havet, Nicolas Nisse

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On interval number in cycle convexity by Julio Araujo, Guillaume Ducoffe, Nicolas Nisse, Karol Suchan

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ON SOME ASPECTS OF DEVELOPMENT OF THE GENERALISED ALLOCATION SCHEME by Andrei Kolchin, Boris Bezrodnyi

“…In this paper we make an attempt to portray the current situation in the probabilistic combinatorics field where so-called generalised allocation scheme has been utilised. …”
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Symmetries of Monocoronal Tilings by Dirk Frettlöh, Alexey Garber

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Chromatic roots as algebraic integers by Adam Bohn

“…At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known as the ``$α +n$ conjecture'' and the ``$nα$ conjecture''. …”
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On the Erdős-Gyárfás Conjecture in Claw-Free Graphs by Nowbandegani Pouria Salehi, Esfandiari Hossein, Haghighi Mohammad Hassan Shirdareh, Bibak Khodakhast

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Poset binomials and rainbow characters by Daniel Bragg, Nathaniel Thiem

“…These coefficients arise naturally in the study of supercharacters of the finite groups of unipotent upper-triangular matrices, whose representation theory is dictated by the combinatorics of set partitions. In particular, we find a natural set of modules for these groups, whose characters have degrees given by $q$-binomials, and whose decomposition in terms of supercharacters are given by poset binomial coefficients. …”
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Seven Études on dynamical Keldysh model by Dmitri V. Efremov, Mikhail N. Kiselev

“…Further we describe the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. …”
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3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs by Xiaolian Liao, Guohua Chen, Shangzhao Li

“…The classification of a block-transitive designs is an important subject on algebraic combinatorics. With the aid of MATLAB software, using the classification theorem of 3-homogeneous permutation groups, we look at the classification problem of block-transitive 7–(v, k, 3) design and prove our main theorem: If the automorphism group of a 7–(v, k, 3) design is block-transitive, then it is neither isomorphic to Affine Type Groups nor Almost Simple Type Groups.…”
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Boolean Discriminant Functions in Symbolic Learning with Subclasses by A. J. Raškinis

“…Finding methods to increase the complexity of the Boolean discriminant functions and to stay within the limits of tractability set by combinatorics is an important task in the field of symbolic machine learning. …”
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