Reply to all Reply to allForward Forward Print Add Gérard to Contacts list Delete this message Report phishing Show original Message text garbled? Gérard H. E. Duchamp to Horzela, Pawel, Penson, Solomon show details 04-Aug (6 days ago) Chers amis, Voici la réponse à Jim Stasheff que je vais envoyer ce soir. Vos remarques (si vous avez un moment) seront les bienvenues. Amitiés Gérard %%%%%%%%%% ANSWER %%%%%%%% Dear Jim, Actually some corrections had already been done. Below, the state of affairs. May I include you in the acknowledgements ? With my best regards Gérard %%%%%%%%%%%%%%%%%%%%%%% >>There was no ^d in the list of affiliations >>The Open U had ^e done. Thank you, this escaped. >>generic after displays: \noindent corrected. >> abstract: in A simplified already done. >>p.1 co-addition instead of the usual comultiplication? yes, I added a footnote because I would like that the reader saw this as a part of the theory of "representative functions" rather than the traditional coproduct. >>reminiscent OF Hoffmann's had been done >>three-parameter (no s) had escaped, thank you. >>the stay of the firs a private house >>Be it's owner --> May ... is she really the OWNER? was it a lodging? changed. >> p.8 as shows --> as is shown changed by "as shown" >> p. 13 We do the extra?? We add the extra? changed by "We make an extra hypothesis" >>p.15 enveloping (one p) and the relation of primitive to enveloping >>should have been recalled at the time you first mention primitive had been done >>first bullet: do not understand what your are trying to say as apprears in Fig5, the letters (generators in the free case) of the monoid are the diagrams that possess only "one" black spot. >>where are crossings and superpositions defined - perhaps I skimmed too fast - diagram 6 only confuses me I have put a footnote in order to make this point clearer. >>p.18 is shifting just a technical computational device or does it mean something? yes, it does. This phenomenon occurs ubiquitously in algebraic combinatorics where it is often due to a translation of the indices in the alphabet of variables (shifted concatenation, shifted shuffle etc...) >>p.19 why is it called phase space meant space of all possible valid configurations. Can replace it by "variety". >>p.21 structure of listS had escaped, thanks. >> p.22 final paragraph: >>how are they structurally different? >>can't any parameter correspond to perturbations? >>do you distinguish deformations from parameters? you're right. I replaced it by "are of different nature". I want to express here that $q_c$ is a deformation of the tensor structure whereas $q_s$ is a perturbation of the law dual to the product. -- Gérard H. E. Duchamp Institut Galilée LIPN-UMR CNRS 7030 ghed@lipn.univ-paris13.fr NY_QV_4_2.pdf 296K View as HTML Download Reply Reply to all Forward Reply Reply to all Reply to allForward Forward Print Add Gérard to Contacts list Delete this message Report phishing Show original Message text garbled? Gérard H. E. Duchamp to jim, Horzela, Pawel, Penson, Solomon show details 05-Aug (5 days ago) Dear Jim, Actually some corrections had already been done. Please find below, the current state of affairs and attached a version taking into account your remarks and others. - Show quoted text - May I include you in the acknowledgements ? With my best regards Gérard %%%%%%%%%%%%%%%%%%%%%%% >>There was no ^d in the list of affiliations >>The Open U had ^e done. Thank you, this escaped. >>generic after displays: \noindent corrected. >> abstract: in A simplified already done. >>p.1 co-addition instead of the usual comultiplication? yes, I added a footnote because I would like that the reader saw this as a part of the theory of "representative functions" rather than the traditional coproduct. >>reminiscent OF Hoffmann's had been done >>three-parameter (no s) had escaped, thank you. >>the stay of the firs a private house >>Be it's owner --> May ... is she really the OWNER? was it a lodging? changed. >> p.8 as shows --> as is shown changed by "as shown" >> p. 13 We do the extra?? We add the extra? changed by "We make an extra hypothesis" >>p.15 enveloping (one p) and the relation of primitive to enveloping >>should have been recalled at the time you first mention primitive had been done >>first bullet: do not understand what your are trying to say as apprears in Fig5, the letters (generators in the free case) of the monoid are the diagrams that possess only "one" black spot. >>where are crossings and superpositions defined - perhaps I skimmed too fast - diagram 6 only confuses me I have put a footnote in order to make this point clearer. >>p.18 is shifting just a technical computational device or does it mean something? yes, it does. This phenomenon occurs ubiquitously in algebraic combinatorics where it is often due to a translation of the indices in the alphabet of variables (shifted concatenation, shifted shuffle etc...) >>p.19 why is it called phase space meant space of all possible valid configurations. Can replace it by "variety". >>p.21 structure of listS had escaped, thanks. >> p.22 final paragraph: >>how are they structurally different? >>can't any parameter correspond to perturbations? >>do you distinguish deformations from parameters? you're right. I replaced it by "are of different nature". I want to express here that $q_c$ is a deformation of the tensor structure whereas $q_s$ is a perturbation of the law dual to the product. -- Gérard H. E. Duchamp Institut Galilée LIPN-UMR CNRS 7030 ghed@lipn.univ-paris13.fr -- Gérard H. E. Duchamp Institut Galilée LIPN-UMR CNRS 7030 ghed@lipn.univ-paris13.fr NY_QV_4_2.pdf 296K View as HTML Download Reply Reply to all Forward Reply Reply to all Reply to allForward Forward Print Add jim to Contacts list Delete this message Report phishing Show original Message text garbled? from jim stasheff hide details 05-Aug (5 days ago) to Gérard H. E. Duchamp date 05-Aug-2007 17:03 subject Re: Answer to Stasheff On Aug 5, 2007, at 6:22 AM, Gérard H. E. Duchamp wrote: > > >>p.19 why is it called phase space > > meant space of all possible valid configurations. Can replace it by "variety". Oh, that I would call configuration space or variety phase space made me think of the cotangent space > > >>p.21 structure of listS > > had escaped, thanks. > > >> p.22 final paragraph: > > >>how are they structurally different? > >>can't any parameter correspond to perturbations? > >>do you distinguish deformations from parameters? > > you're right. I replaced it by "are of different nature". I want to express here that $q_c$ is a > > deformation of the tensor structure whereas $q_s$ is a perturbation of the law dual to the > > product. ah, much clearer but do you distinguish deformation from perturbation jim > Reply Forward Invite jim to Gmail Reply Reply to all Reply to allForward Forward Print Add Gérard to Contacts list Delete this message Report phishing Show original Message text garbled? Gérard H. E. Duchamp to jim, Horzela, Pawel, Penson, Solomon show details 10:37 (7 minutes ago) Dear Jim, I apologize for not having replied sooner. In fact, I had to help organize a Congress in Combinatoral Physics which will be held in Cracow soon (end of november, you will receive an invitation ASAP). >but do you distinguish deformation from perturbation In fact, the difference is not completely worked out mathematically (and doesn't have to be in this paper). Say that it can be checked (in many cases in combinatorics) that one can perturbate the basic coproduct \Delta(x)=x\otimes 1+1\otimes x (dual to the shuffle coproduct) by a "little something" (which is often "q" times another coproduct, as in [16]). In the case of deformations of laws, one doesn't have necessarily a (combinatorially) nice dual law, but we have interpolations between known laws (as in (D22) below, I will add this reference). Best regards Gérard %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \bibitem{D22} Duchamp G., Klyachko A., Krob D., Thibon J.Y., {\it Noncommutative symmetric functions III: Deformations of Cauchy and convolution algebras} Discrete Mathematics and Theoretical Computer Science Vol. {\bf 2} (1998). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - Show quoted text - On 05/08/07, jim stasheff < jds@math.upenn.edu> wrote: On Aug 5, 2007, at 6:22 AM, Gérard H. E. Duchamp wrote: > > >>p.19 why is it called phase space > > meant space of all possible valid configurations. Can replace it by "variety". Oh, that I would call configuration space or variety phase space made me think of the cotangent space > > >>p.21 structure of listS > > had escaped, thanks. > > >> p.22 final paragraph: > > >>how are they structurally different? > >>can't any parameter correspond to perturbations? > >>do you distinguish deformations from parameters? > > you're right. I replaced it by "are of different nature". I want to express here that $q_c$ is a > > deformation of the tensor structure whereas $q_s$ is a perturbation of the law dual to the > > product. ah, much clearer but do you distinguish deformation from perturbation jim > - Show quoted text - -- Gérard H. E. Duchamp Institut Galilée LIPN-UMR CNRS 7030 ghed@lipn.univ-paris13.fr