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1. Full Text On cardinalities of k-abelian equivalence classes
by Karhumäki, Juhani and Puzynina, Svetlana and Rao, Michaël and Whiteland, Markus A
Theoretical Computer Science, ISSN 0304-3975, 01/2017, Volume 658, pp. 190 - 204
Two words and are -abelian equivalent if for each word of length at most , occurs equally many times as a factor in both and . The notion of -abelian... 
Hamiltonian paths | Necklaces | Gray codes | de Bruijn graph | k-abelian equivalence | COMPUTER SCIENCE, THEORY & METHODS | Jewelry | Lower bounds | Equivalence | Upper bounds | Alphabets | Binary codes | Graphs | Decomposition | Joints | Computer Science | Discrete Mathematics
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2. Full Text Equivalence classes of Dyck paths modulo some statistics
by Baril, Jean-Luc and Petrossian, Armen
Discrete Mathematics, ISSN 0012-365X, 04/2015, Volume 338, Issue 4, pp. 655 - 660
We investigate new equivalence relations on the set of Dyck paths relatively to the three statistics of double rises, peaks and valleys. Two Dyck paths are... 
Equivalence relation | Motzkin and Fibonacci sequences | Valley | Catalan | Dyck path | Peak | Statistics | Rise | MATHEMATICS | Functions (mathematics) | Equivalence | Mathematical analysis | Valleys | Combinatorics | Mathematics
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3. Full Text Equivalence classes of ballot paths modulo strings of length 2 and 3
by Manes, K and Sapounakis, A and Tasoulas, I and Tsikouras, P
Discrete Mathematics, ISSN 0012-365X, 10/2016, Volume 339, Issue 10, pp. 2557 - 2572
Two paths are equivalent modulo a given string , whenever they have the same length and the positions of the occurrences of are the same in both paths. This... 
Ballot path | Dyck path | String | MATHEMATICS | DYCK PATHS | STATISTICS | ENUMERATION | Equivalence | Mathematical analysis | Strings
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4. Equivalence classes of Motzkin paths modulo a pattern of length at most two
by Baril, Jean-Luc and Petrossian, Armen
Journal of Integer Sequences, 2015, Volume 18, Issue 7
Equivalence relation | Motzkin path | Statistics
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5. Full Text The cospectral equivalence classes of graphs having an isolated vertex
by Wang, Jianfeng and Huang, Qiongxiang and Liu, Yongzhi and Liu, Ruying and Ye, Chengfu
Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 57, Issue 10, pp. 1638 - 1644
Let be the characteristic polynomial of a graph . Two graphs and are cospectral, denoted by , if . By we denote the cospectral equivalence class determined by... 
Adjacency spectrum | Cospectral graph | Cospectral equivalence class | Spectral radius | DS-graph | PATH | MATHEMATICS, APPLIED | INDEX | SPECTRAL CHARACTERIZATION | ROOT-2+ROOT-5
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6. Full Text The minimum rank of matrices and the equivalence class graph
by Fernandes, Rosàrio and Perdigão, Cecı´lia
Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 427, Issue 2, pp. 161 - 170
For a given connected (undirected) graph , the minimum rank of is defined to be the smallest possible rank over all hermitian matrices whose th entry is... 
Graphs | Minimum rank | 05C50 | Hermitian matrices | 15A18 | hermitian matrices | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | graphs | minimum rank | MAXIMUM MULTIPLICITY | PATH COVER NUMBER
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7. Full Text A combinatorial equivalence relation for formal power series
by Cheon, Gi-Sang and Jin, Sung-Tae and Shapiro, Louis W
Linear Algebra and Its Applications, ISSN 0024-3795, 02/2016, Volume 491, pp. 123 - 137
In this paper we examine an equivalence relation on the set of formal power series with nonzero constant term. This is done both in terms of functional... 
Riordan matrix | Extended Riordan matrix | Equivalence class | Lattice path | Functional equation | MATHEMATICS | MATHEMATICS, APPLIED | NUMBERS | RIORDAN MATRICES | ARRAYS
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8. Full Text Equivalence Classes for the mu-Coefficient of Kazhdan-Lusztig Polynomials in S-n
by Warrington, GS
EXPERIMENTAL MATHEMATICS, ISSN 1058-6458, 2011, Volume 20, Issue 4, pp. 457 - 466
We study equivalence classes relating to the Kazhdan-Lusztig mu(x, w) coefficients in order to help explain the scarcity of distinct values. Each class is... 
MATHEMATICS | LATTICE PATHS | PERMUTATIONS | SCHUBERT VARIETIES | Kazhdan-Lusztig polynomials | mu-coefficient | equivalence classes
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9. Full Text Enumeration of Łukasiewicz paths modulo some patterns
by Baril, Jean-Luc and Kirgizov, Sergey and Petrossian, Armen
Discrete Mathematics, ISSN 0012-365X, 04/2019, Volume 342, Issue 4, pp. 997 - 1005
For any pattern of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length where two paths are equivalent whenever the occurrence... 
Equivalence relation | Łukasiewicz path | Motzkin path | Dyck path | Patterns | Lukasiewicz path | STRINGS | MATHEMATICS | VALLEYS | PEAKS | DYCK | EQUIVALENCE CLASSES
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10. Full Text Finding the k shortest simple paths
: A new algorithm and its implementation
by Hershberger, John and Maxel, Matthew and Suri, Subhash
ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 11/2007, Volume 3, Issue 4, pp. 45 - es
We describe a new algorithm to enumerate the k shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on... 
replacement paths | path equivalence class | Loop-free paths | directed paths | Directed paths | Path equivalence class | Replacement paths | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS
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11. An efficient timer based minimum path D-equivalence CDS construction for wireless adhoc networks
by Ramya, P and Gopalakrishnan, V
Indian Journal of Science and Technology, ISSN 0974-6846, 2015, Volume 8, pp. 24 - 32
Shortest path | D-equivalence classes | Connected dominating set (CDS) | Minimum routing cost cds (A- MOC-CDS) | Minimum support tree
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12. Full Text Local Learning Approaches for Finding Effects of a Specified Cause and Their Causal Paths
by Liu, Yue and Cai, Zheng and Liu, Chunchen and Geng, Zhi
ACM Transactions on Intelligent Systems and Technology (TIST), ISSN 2157-6904, 11/2019, Volume 10, Issue 5, pp. 1 - 15
Causal networks are used to describe and to discover causal relationships among variables and data generating mechanisms. There have been many approaches for... 
causes and effects | structural learning | causal networks | Causal paths | COMPUTER SCIENCE, INFORMATION SYSTEMS | EQUIVALENCE CLASSES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
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13. Full Text On the spectral characterization of the union of complete multipartite graph and some isolated vertices
by Ma, Haicheng and Ren, Haizhen
Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 24, pp. 3648 - 3652
A graph is said to be determined by its adjacency spectrum (DS for short) if there is no other non-isomorphic graph with the same spectrum. In this paper, we... 
Adjacency spectrum | Cospectral equivalence class | Cospectral graphs | DS-graph | PATH | MATHEMATICS | TREES | INDEX | Cospectral equivalence
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14. Full Text Semigroup theory of symmetry
by Rosenfeld, Vladimir R and Nordahl, Thomas E
Journal of Mathematical Chemistry, ISSN 0259-9791, 10/2016, Volume 54, Issue 9, pp. 1758 - 1776
Symmetry is one of the most fundamental concepts of all nature. We discuss the general theory of symmetry based on theory of semigroups. This includes and... 
Orbit | Semifractal | Hidden regularities | Semigroup | Monoid | Theoretical and Computational Chemistry | Chemistry | Hidden symmetry | Fractal | Physical Chemistry | Endomorphism monoid | Inverse semigroup | Color symmetry | Quasicrystal | Automorphism (symmetry) group | Math. Applications in Chemistry | PATHS | MONOIDS | ENDOMORPHISMS | CHEMISTRY, MULTIDISCIPLINARY | GRAPHS | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | REGULARITY | QUASI-CRYSTALS | EQUIVALENCE CLASSES | Research | Mathematical research | Group theory | Symmetry
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15. Full Text Multiple Testing and Error Control in Gaussian Graphical Model Selection
by Mathias Drton and Michael D. Perlman
Statistical Science, ISSN 0883-4237, 8/2007, Volume 22, Issue 3, pp. 430 - 449
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by... 
Error rates | Gaussian distributions | Statistical graphs | Directed acyclic graphs | Correlations | P values | Markov models | Covariance matrices | Modeling | Vertices | Acyclic directed graph | Covariance graph | Graphical model | Bidirected graph | Concentration graph | Undirected graph | Multiple testing | DAG | Chain graph | Bayesian network | CHAIN GRAPHS | ASSOCIATIONS | PATH DIAGRAMS | COVARIANCE-SELECTION | STATISTICS & PROBABILITY | NETWORKS | bidirected graph | FALSE DISCOVERY RATE | MARKOV EQUIVALENCE CLASSES | concentration graph | chain graph | graphical model | multiple testing | MULTIDIMENSIONAL CONTINGENCY-TABLES | undirected graph | covariance graph | MULTIVARIATE TIME-SERIES | EXPRESSION | acyclic directed graph
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16. Degenerate parametric amplification of squeezed photons: Explicit solutions, statistics, means and variances
by Acosta-Humánez, P.B and Kryuchkov, S.I and Suazo, E and Suslov, S.K
Journal of Nonlinear Optical Physics and Materials, ISSN 0218-8635, 06/2015, Volume 24, Issue 2, pp. 1550021 - 1-1550021-27
In the Schrodinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multi-parameter squeezed input... 
Ince equation | interaction picture | Wigner function | Ermakov-type system | degenerate parametric amplifier | differential Galois theory | Kovacic algorithm | Time-dependent Schrödinger equation | PHYSICS, APPLIED | MINIMUM-UNCERTAINTY PACKETS | COHERENT STATES | ELECTROMAGNETIC-FIELD | RADIATION-FIELD | Time-dependent Schrodinger equation | HARMONIC-OSCILLATORS | THERMAL NOISE | OPTICS | PATH-INTEGRAL APPROACH | NONLINEAR OPTICS | QUANTUM-THEORY | EQUIVALENCE CLASSES | Operators | Evolution | Mathematical models | Photons | Transformations | Schroedinger equation | Representations | Statistics
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17. Full Text Hierarchical Strategy for Identifying Active Chemotype Classes in Compound Databases
by Medina-Franco, Jose Luis and Petit, Joachim and Maggiora, Gerald M
Chemical Biology & Drug Design, ISSN 1747-0277, 06/2006, Volume 67, Issue 6, pp. 395 - 408
A general methodology is presented for analyzing patterns of activity in compound databases, which is based on the use of structural chemotypes and provides a... 
chemotype-enrichment plots | chemotypes | NCI AIDS database | paths of activity | equivalence classes | parent-child relationships | chemotype‐enrichment plots | parent–child relationships | Equivalence classes | Paths of activity | Chemotype-enrichment plots | Parent-child relationships | Chemotypes | BIOCHEMISTRY & MOLECULAR BIOLOGY | REVERSE-TRANSCRIPTASE | SETS | IMMUNODEFICIENCY-VIRUS TYPE-1 | INHIBITORS | SOFTWARE | Models, Molecular | Chemistry Techniques, Analytical - methods | Sensitivity and Specificity | Computational Biology | Databases, Factual | Study and teaching | Analysis | Databases
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18. Full Text Analysis of algorithms for listing equivalence classes of k-ary strings
by Proskurowski, Andrzej and Ruskey, Frank and Smith, Malcolm
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 1998, Volume 11, Issue 1, pp. 94 - 109
We give efficient algorithms for listing equivalence classes of k-ary strings under reversal and permutation of alphabet symbols. As representative of each... 
Combinatorial generation | k-paths | Stirling numbers | K-ary strings | Restricted growth function | GENERATING NECKLACES | COLORS | MATHEMATICS, APPLIED | combinatorial generation | restricted growth function | k-ary strings | BEADS
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19. Full Text Beyond the LAN: Ethernet's Evolution into the Public Network
by KELLETT, PAUL
Fiber and Integrated Optics, ISSN 0146-8030, 01/2003, Volume 22, Issue 5, pp. 289 - 303
This article details the evolution of Ethernet into Gigabit Ethernet and how this LAN-based technology has undergone major transformations over time. From its... 
1-gigabit ethernet | Single Mode Fiber (SMF) | Frame Check Sequence (FCS) | Dense Wavelength Division Multiplexing (DWDM) | fiber channel | Shielded Twisted Pair (STP) | Synchronous Optical Networks (SONET) | Add-Drop Multiplexor (ADM) | Time Division Multiplexing (TDM) | Media Independent Interface (MII) | Switched Virtual Circuits (SWC) | Physical Layer (PHY) | Label Switched Router (LSR) | Point-to-Point Protocol (PPP) | Link Capacity Adjustment Scheme (LCAS) | Resilient Packet Rings (RPR) | Virtual Concatenation Group (VCG) | Unshielded Twisted Pair (UTP) | SDH Virtual Container (SDH-VC) | ethernet | Physical Medium Dependents (PMDs) | Carrier Sense Multiple Access with Collision Detection (CSMA/CD) | Optical Cross Connect (OXC) | Inter-Packet Gap (IPG) | Optical Circuit (OC) | Packet Over SONET (POS) | Ethernet Over SONET (EOS) | Local Area Networks (LAN) | Generalized Multi-Protocol Label Switching (GMPLS) | Permanent Virtual Circuits (PVC) | Label Edge Router (LER) | Wide Wave Division Multiplexing (WWDM) | Synchronous Payload Envelope (SPE) | Forward Equivalence Class (FEC) | 10-gigabit ethernet | Gigabit Media Independent Interface (GMII) | Network Interface Card (NIC) | Internet Protocol (IP) | Virtual Concatenation (VC) | token ring | Virtual Private Network (VPN) | Label Switched Path (LSP) | Physical Coding Sublayer (PCS) | Multiple Protocol Label Switching (MPLS) | Media Access Control (MAC) | Quality of Service (QOS) | Reconciliation Sublayer (RS) | Metropolitan Area Networks (MAN) | Physical Medium Attachment (PMA) | Wide Area Networks (WAN) | Synchronous Digital Hierarchy (SDH) | Generic Framing Procedure (GFP) | OPTICS
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20. Full Text Beyond the LAN: Ethernet's evolution into the public network
by Kellett, Paul
Fiber and Integrated Optics, ISSN 0146-8030, 2003, Volume 22, Issue 5, pp. 289 - 303
1-gigabit ethernet | Permanent virtual circuits (PVC) | Synchronous digital hierarchy (SDH) | Synchronous payload envelope (SPE) | Media access control (MAC) | Label switched router (LSR) | Ethernet over SONET (EOS) | Generic framing procedure (GFP) | Add-drop multiplexor (ADM) | Virtual concatenation (VC) | Wide wave division multiplexing (WWDM) | Carrier sense multiple access with collision detection (CSMA/CD) | Label edge router (LER) | Switched virtual circuits (SWC) | Network interface card (NIC) | Virtual private network (VPN) | Gigabit media independent interface (GMII) | Physical coding sublayer (PCS) | Frame check sequence (FCS) | Ethernet | Optical circuit (OC) | SDH virtual container (SDH-VC) | Media independent interface (MII) | Inter-packet gap (IPG) | Physical medium dependents (PMDs) | Virtual concatenation group (VCG) | Local area networks (LAN) | Physical medium attachment (PMA) | Link capacity adjustment scheme (LCAS) | Fiber channel | Optical cross connect (OXC) | Single mode fiber (SMF) | 10-gigabit ethernet | Packet over SONET (POS) | Forward equivalence class (FEC) | Synchronous optical networks (SONET) | Multiple protocol label switching (MPLS) | Physical layer (PHY) | Shielded twisted pair (STP) | Dense wavelength division multiplexing (DWDM) | Internet protocol (IP) | Point-to-point protocol (PPP) | Metropolitan area networks (MAN) | Label switched path (LSP) | Reconciliation sublayer (RS) | Generalized multi-protocol label switching (GMPLS) | Token ring | Quality of service (QOS) | Time division multiplexing (TDM) | Wide area networks (WAN) | Resilient packet rings (RPR) | Unshielded twisted pair (UTP)
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