On a weight system conjecturally related to

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• 作者：E. Kulakova ^{lenaetopena@gmail.com" class="auth_mail} ; S. Lando ^{lando@hse.ru" class="auth_mail} ; T. Mukhutdinova ^{kassalanche@gmail.com" class="auth_mail} ; G. Rybnikov ^{grigory.rybnikov@gmail.com" class="auth_mail}
• 刊名：European Journal of Combinatorics
• 出版年：October 2014
• 年：2014
• 卷：41
• 期：Complete
• 页码：266-277
• 全文大小：910 K

文摘

We introduce a new series id="mmlsi26" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si26.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=92feb35187cab8efe417aeec8e58f1aa" title="Click to view the MathML source">R_kiner hidden">i26.gif" overflow="scroll">i>Ri>i>ki>, id="mmlsi27" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si27.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=377e1b9fb1c2e52107558c23d0751c56" title="Click to view the MathML source">k=2,3,4,…iner hidden">i27.gif" overflow="scroll">i>ki>=2,3,4,…, of integer valued weight systems. The value of the weight system id="mmlsi28" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si28.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=095bae21a3124c535f3b11caad197a6d" title="Click to view the MathML source">R_kiner hidden">i28.gif" overflow="scroll">i>Ri>i>ki> on a chord diagram is a signed number of cycles of even length id="mmlsi29" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si29.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=3c9029b1c4191c9d2219bd53ecea35e4" title="Click to view the MathML source">2kiner hidden">i29.gif" overflow="scroll">2i>ki> in the intersection graph of the diagram. We show that this value depends on the intersection graph only. We check that for small orders of the diagrams, the value of the weight system id="mmlsi30" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si30.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=6ba623645007bec05f6aee249b21ec41" title="Click to view the MathML source">R_kiner hidden">i30.gif" overflow="scroll">i>Ri>i>ki> on a diagram of order exactly id="mmlsi31" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si31.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=d67ae1b02999ff0e72b78349638c0b7c" title="Click to view the MathML source">2kiner hidden">i31.gif" overflow="scroll">2i>ki> coincides with the coefficient of id="mmlsi32" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si32.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=439da8f3d79ecf673458f50a733d5b33" title="Click to view the MathML source">c^kiner hidden">i32.gif" overflow="scroll">i>ci>i>ki> in the value of the id="mmlsi33" class="mathmlsrc">ixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669814000687&_mathId=si33.gif&_user=111111111&_pii=S0195669814000687&_rdoc=1&_issn=01956698&md5=acf2c4d0211e9d09e03f87cbb13e1f05" title="Click to view the MathML source">sl₂iner hidden">i33.gif" overflow="scroll">i mathvariant="fraktur">si>i>li>2-weight system on the projection of the diagram to primitive elements.