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Canonical measure assignments

Steve Jackson, Benedikt Löwe
2013 Journal of Symbolic Logic (JSL)  
projective ordinals).  ...  We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal κ < ℵ ε0 in a recursive definition of a canonical measure assignment.  ...  Given a set X of labels, we call a pair T, ℓ an X -labelled tree if T is a tidy tree and ℓ : T \{•} → X .  ... 
doi:10.2178/jsl.7802040 fatcat:yjtqqozzxvdx7cdqrymf3camda

A Gray Code for the Ideals of a Forest Poset

Y. Koda, F. Ruskey
1993 Journal of Algorithms  
On each iteration, the rst algorithm does a partial traversal of the current ideal being listed and runs in time O(nN), where N is the number of ideals of the poset.  ...  The second algorithm mimics the rst, but eliminates the traversal and runs in time O(N).  ...  This will follow as a consequence of more general results about the ordinal and direct sums of posets. A necessary condition for the existence of a Hamiltonian path in J(P) is that jd(P)j 1.  ... 
doi:10.1006/jagm.1993.1044 fatcat:xwunyyhq25erncl5aoc7mmfwke

On the Exploration of the Solution Space in Analog Placement With Symmetry Constraints

F. Balasa, S.C. Maruvada, K. Krishnamoorthy
2004 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
This paper presents a novel exploration technique for analog placement operating on a subset of tree representations of the layout-called symmetric-feasible, where the typical presence of an arbitrary  ...  This superior efficiency is partly due to the use of segment trees, a data structure introduced by Bentley, mainly used in computational geometry.  ...  It can be seen quite easily that there is a one-to-one mapping between the set of (labeled) binary trees with nodes and the set of symmetric-feasible binary trees with nodes.  ... 
doi:10.1109/tcad.2003.822132 fatcat:xeunmogt4vcthnszqdrg2httb4

Open Questions in Reverse Mathematics

Antonio Montalbán
2011 Bulletin of Symbolic Logic  
We also mention some of the areas of reverse mathematics that are starting to be developed and where interesting open question may be found.  ...  We present a list of open questions in reverse mathematics, including some relevant background information for each question.  ...  Let 2 <N be the full binary tree, and let [2 <N ] n denote the set of n-tuples of comparable nodes of 2 <N .  ... 
doi:10.2178/bsl/1309952320 fatcat:maim2j6vovfcpjjkrzm7xeicqi

The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion [article]

Eric van Fossen Conrad, Philippe Flajolet
2005 arXiv   pre-print
The combinatorial models are related to but different from models of elliptic functions earlier introduced by Viennot, Flajolet, Dumont, and Françon.  ...  Elliptic functions considered by Dixon in the nineteenth century and related to Fermat's cubic, x^3+y^3=1, lead to a new set of continued fraction expansions with sextic numerators and cubic denominators  ...  We are thankful to Hjalmar Rosengren for first pointing us to the works of Lindqvist and Peetre-Peter Lindqvist then very kindly offered a wealth of mathematical and historical material relative to Lundberg's  ... 
arXiv:math/0507268v1 fatcat:k2te2zeyw5hxdg2nby27ysts4y

Towards combinatorial clustering: preliminary research survey [article]

Mark Sh. Levin
2015 arXiv   pre-print
assessment of objects and object proximities (i.e., scales, comparison, aggregation issues), (iii) basic approaches to evaluation of local quality characteristics for clusters and total quality characteristics  ...  The paper describes clustering problems from the combinatorial viewpoint.  ...  Clustering of multi-neighbor nodes B 1 (complexity estimate equals about O(|B 1 | 2 ) (about O((n ). Stage 4. Stop.Fig. 4.17. Multi-beam antenna system Slot 1 Slot 2 ...  ... 
arXiv:1505.07872v1 fatcat:ih4b72afjrcrbmp5yrgtnnwga4

Learning Ordinal Preferences on Multiattribute Domains: The Case of CP-nets [chapter]

Yann Chevaleyre, Frédéric Koriche, Jérôme Lang, Jérôme Mengin, Bruno Zanuttini
2010 Preference Learning  
In this paper, we investigate the problem of learning ordinal preference orderings over discrete multi-attribute, or combinatorial, domains.  ...  the target CP-net. * Partially supported by the ANR projects CANAR (ANR-06-BLAN-0383-02) and PHAC (ANR-05-BLAN-0384-01  ...  In all the contexts we considered above, the system has to learn preferences of a user over a set of alternatives that possesses a combinatorial structure.  ... 
doi:10.1007/978-3-642-14125-6_13 fatcat:wmcxae2gcvejdgaqpdge4uuar4

Infinitary Combinatory Reduction Systems

Jeroen Ketema, Jakob Grue Simonsen
2011 Information and Computation  
We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting.  ...  The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary λ-calculus are special cases.  ...  Acknowledgments The authors extend their thanks to the anonymous referees for their diligent work and many comments that have led to substantial improvements in the readability of the paper.  ... 
doi:10.1016/j.ic.2011.01.007 fatcat:b54kclljc5fc5kxqpndfahjgea

Infinitary Combinatory Reduction Systems [chapter]

Jeroen Ketema, Jakob Grue Simonsen
2005 Lecture Notes in Computer Science  
We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting.  ...  The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary λ-calculus are special cases.  ...  Acknowledgments The authors extend their thanks to the anonymous referees for their diligent work and many comments that have led to substantial improvements in the readability of the paper.  ... 
doi:10.1007/978-3-540-32033-3_32 fatcat:utgdfhexefhyhnl2yftwei5uqy

Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints [article]

Daniela Battaglino
2014 arXiv   pre-print
Noting that this generating function can be expressed in terms of the Fibonacci polynomials, we describe a bijection between the class of k-parallelogram polyominoes and the class of planted planar trees  ...  In both approaches our results can be used to treat open problems related to polyominoes as well as other combinatorial objects.  ...  So, from now on, when we deal of trees, we mean labeled trees as we have just seen.  ... 
arXiv:1405.3146v1 fatcat:rzvmlsmzlng2zpozrvpxteea3m

Extended term rewriting systems [chapter]

Jan Willem Klop, Roel Vrijer
1991 Lecture Notes in Computer Science  
In this paper we will consider some extensions of the usual term rewrite format, namely: term rewriting with conditions, infmi~y term rewriting and term rewriting with bound variables.  ...  Rather than aiming at a complete survey, we discuss some aspects of these three extensions.  ...  We thank Aart Middeldorp and Vincent van Oostrom for carefully reading the manuscript and suggesting improvements.  ... 
doi:10.1007/3-540-54317-1_79 fatcat:g7vqrgyaafabtgesdd2mvgihnq

The first omega alephs: from simplices to trees of trees to higher walks [article]

Jeffrey Bergfalk
2021 arXiv   pre-print
In the course of this work, we describe simplicial characterizations of the ordinals ω_n, higher-dimensional generalizations of coherent Aronszajn trees, bases for critical inverse systems over large index  ...  These constructions and arguments are undertaken entirely within a 𝖹𝖥𝖢 framework; at their heart is a simple, finitely iterable technique of compounding C-sequences.  ...  He would like to thank his advisor, Justin Tatch Moore, and the rest of his thesis committee, Jim West and Slawek Solecki, for their support, instruction, and patience throughout the course of its composition  ... 
arXiv:2008.03386v2 fatcat:z352uqtqi5f2hnllweqz4obege

Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions [article]

J.-C. Novelli, J.-Y. Thibon
2020 arXiv   pre-print
In the same way as planar binary trees can be interpreted as sylvester classes of permutations, we obtain (m+1)-ary trees as sylvester classes of what we call m-permutations.  ...  On another hand, the Tamari order is related to the product in the Loday-Ronco Hopf algebra of planar binary trees.  ...  -This research has been partially supported by the project CARMA of the French Agence Nationale de la Recherche.  ... 
arXiv:1403.5962v3 fatcat:25vfcylaxnh6jadkwyjeiyzpr4

Reverse Mathematics and Well-ordering Principles [chapter]

Michael Rathjen, Andreas Weiermann
2011 Computability in Context  
This was first proved by Friedman (see [8] ) using recursion-theoretic and combinatorial methods.  ...  The paper is concerned with generally Π 1 2 sentences of the form " if X is well ordered then f (X) is well ordered", where f is a standard proof theoretic function from ordinals to ordinals.  ...  The proof of Theorem 1.3 uses rather sophisticated recursion-theoretic results about linear orderings and is quite combinatorial.  ... 
doi:10.1142/9781848162778_0011 fatcat:dcuui4tfwzdajevxxihdeecygm

Tameness of Pseudovariety Joins Involving ${\sf R}$

Jorge Almeida, José Carlos Costa, Marc Zeitoun
2005 Monatshefte für Mathematik (Print)  
In particular, we show that the pseudovariety V ∨ W is (completely) κ-tame when V is a subpseudovariety of J with decidable κ-word problem and W is (completely) κ-tame.  ...  In this paper, we establish several decidability results for pseudovariety joins of the form V ∨ W, where V is a subpseudovariety of J or the pseudovariety R. Here, J (resp.  ...  Acknowledgment The authors would like to thank the anonymous referees for their comments which significantly contributed to improve the readability of the paper.  ... 
doi:10.1007/s00605-005-0324-1 fatcat:hz5zkjre4jf4veikvxoric6wma
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