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Bijections between directed animals, multisets and Grand-Dyck paths [article]

Jean-Luc Baril, David Bevan, Sergey Kirgizov
<span title="2019-11-20">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Then we give constructive bijections between directed animals, multisets with no consecutive elements and Grand-Dyck paths avoiding the pattern DUD, and we show how classical and novel statistics are transported  ...  We present the bivariate generating function for n-multisets of [k] with no consecutive elements. For n=k, these multisets have the same enumeration as directed animals in the square lattice.  ...  Φ −1 Ψ between directed animals and multisets via Grand-Dyck paths.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1906.11870v2">arXiv:1906.11870v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dzo6vnl46jc5ziuyo43rzfj62i">fatcat:dzo6vnl46jc5ziuyo43rzfj62i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200828233000/https://arxiv.org/pdf/1906.11870v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/08/5708c8a0605b3278299defeb8f5d5e4fada38cdf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1906.11870v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Bijections between Directed Animals, Multisets and Grand-Dyck Paths

Jean-Luc Baril, David Bevan, Sergey Kirgizov
<span title="2020-04-17">2020</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v5dyak6ulffqfara7hmuchh24a" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
Then we give constructive bijections between directed animals, multisets with no consecutive elements and Grand-Dyck paths avoiding the pattern $DUD$, and we show how classical and novel statistics are  ...  We present the bivariate generating function for $n$-multisets of $[k]$ with no consecutive elements. For $n=k$, these multisets have the same enumeration as directed animals in the square lattice.  ...  Acknowledgements We would like to thank the anonymous referees for their helpful comments and suggestions. References  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/8826">doi:10.37236/8826</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xisl2zpefzes7olqlspxup7qcy">fatcat:xisl2zpefzes7olqlspxup7qcy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200508054256/https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p10/8067" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/76/74/7674ea9809ebee258ee60685b48c01bcfe1c54de.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/8826"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Correct and Efficient Accelerator Programming (Dagstuhl Seminar 13142)

Bernadette Charron-Bost, Stepahn Merz, Andrey Rybalchenko, Josef Widder, Albert Cohen, Alastair Donaldson, Marieke Huisman, Joost-Pieter Katoen, Stephen Kobourov, Martin Nöllenburg, Monique, Sergiu Hart (+2 others)
<span title="">2013</span> <span class="release-stage">unpublished</span>
I discuss the problem definition, the variations and different objectives, and the pitfalls. I also survey the classical algorithms of Douglas and Peucker; Imai and Iri; and of Chan and Chin.  ...  In the last part I also mention an algorithm of Drysdale, Rote, and Sturm [1] for smooth (tangent-continuous) approximation by biarcs.  ...  drawings[1]: Brinkman graph, Dyck graph, and F40 (dodecahedron double cover).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m7452gw4cvecbd2vi6w3uha5ai">fatcat:m7452gw4cvecbd2vi6w3uha5ai</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180520192547/http://drops.dagstuhl.de/opus/volltexte/2013/4263/pdf/dagrep-v003-i004-complete.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/c3/e1c3d4b86a43aeb5f252d61e2b468f69c2585f88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>