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## Filters

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Canonical measure assignments

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 . ...

##
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A Gray Code for the Ideals of a Forest Poset

1993
*
Journal of Algorithms
*

On each

doi:10.1006/jagm.1993.1044
fatcat:xwunyyhq25erncl5aoc7mmfwke
*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. ...##
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On the Exploration of the Solution Space in Analog Placement With Symmetry Constraints

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

doi:10.1109/tcad.2003.822132
fatcat:xeunmogt4vcthnszqdrg2httb4
*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. ...##
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Open Questions in Reverse Mathematics

2011
*
Bulletin of Symbolic Logic
*

We also mention some

doi:10.2178/bsl/1309952320
fatcat:maim2j6vovfcpjjkrzm7xeicqi
*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 . ...##
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The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion
[article]

2005
*
arXiv
*
pre-print

The

arXiv:math/0507268v1
fatcat:k2te2zeyw5hxdg2nby27ysts4y
*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 ...##
###
Towards combinatorial clustering: preliminary research survey
[article]

2015
*
arXiv
*
pre-print

assessment

arXiv:1505.07872v1
fatcat:ih4b72afjrcrbmp5yrgtnnwga4
*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 ... ...##
###
Learning Ordinal Preferences on Multiattribute Domains: The Case of CP-nets
[chapter]

2010
*
Preference Learning
*

In this paper, we investigate the problem

doi:10.1007/978-3-642-14125-6_13
fatcat:wmcxae2gcvejdgaqpdge4uuar4
*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. ...##
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Infinitary Combinatory Reduction Systems

2011
*
Information and Computation
*

We define infinitary

doi:10.1016/j.ic.2011.01.007
fatcat:b54kclljc5fc5kxqpndfahjgea
*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. ...##
###
Infinitary Combinatory Reduction Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

We define infinitary

doi:10.1007/978-3-540-32033-3_32
fatcat:utgdfhexefhyhnl2yftwei5uqy
*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. ...##
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Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints
[article]

2014
*
arXiv
*
pre-print

Noting that this generating function can be expressed in terms

arXiv:1405.3146v1
fatcat:rzvmlsmzlng2zpozrvpxteea3m
*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. ...##
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Extended term rewriting systems
[chapter]

1991
*
Lecture Notes in Computer Science
*

In this paper we will consider some extensions

doi:10.1007/3-540-54317-1_79
fatcat:g7vqrgyaafabtgesdd2mvgihnq
*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. ...##
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The first omega alephs: from simplices to trees of trees to higher walks
[article]

2021
*
arXiv
*
pre-print

In the course

arXiv:2008.03386v2
fatcat:z352uqtqi5f2hnllweqz4obege
*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 ...##
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Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions
[article]

2020
*
arXiv
*
pre-print

In the same way as planar

arXiv:1403.5962v3
fatcat:25vfcylaxnh6jadkwyjeiyzpr4
*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. ...##
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Reverse Mathematics and Well-ordering Principles
[chapter]

2011
*
Computability in Context
*

This was first proved by Friedman (see [8] ) using recursion-theoretic

doi:10.1142/9781848162778_0011
fatcat:dcuui4tfwzdajevxxihdeecygm
*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*. ...##
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Tameness of Pseudovariety Joins Involving ${\sf R}$

2005
*
Monatshefte für Mathematik (Print)
*

In particular, we show that the pseudovariety V ∨ W is (completely) κ-tame when V is a subpseudovariety

doi:10.1007/s00605-005-0324-1
fatcat:hz5zkjre4jf4veikvxoric6wma
*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. ...
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