Báo cáo toán học: "A strengthening of Brooks’ Theorem for line graphs" doc

... another proof of the following result (see [14] for the original proof and [17] for further r emarks and adiﬀerent proof). Theorem 3 (King, Reed and Vetta [14]). If G is the line graph of a multigraph, ... of G, respectively. Thus Brooks’ Theorem holds for line graphs of multigraphs in much stronger form. Using similar methods wethen prove that if G is th e line graph of a multigraph with χ(G) ... counterexamplesthat are the line graph of a multigraph f or ∆(G) ≥ 9. This is tight since the abovecounterexample for ∆(G) = 8 is a line graph of a multigraph. Theorem 5. If G is the line graph of a multigraph...

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Báo cáo toán học: "A Generalization of Gosper’s Algorithm to Bibasic" docx

... of allcoefficient-denominators of ¯P,letg denote the greatest common divisor of all coefficients of l ·¯P , and define z := g/l. Then, for P∗:= z−1·¯P , the bibasic monic decomposition of ... problem of q-hypergeometric tele-scoping can be treated along the same lines as the q = 1 case by making use of a q-version of GFF. Built on these concepts, a Mathematica implementation of q-analogues ... “overlaps” of bibasic factorials that violate length maximality. The following theorem states that, as in the q-hypergeometric case, the bibasic GFF-form is unique and thus providesa canonical form.Theorem...

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Báo cáo toán học: " New proofs of Schur-concavity for a class of symmetric functions" potx

... upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.New proofs of Schur-concavity for a class of symmetric functionsJournal of Inequalities and Applications ... below). For information about publishing your research in Journal of Inequalities and Applications go tohttp://www.journalofinequalitiesandapplications.com/authors/instructions/ For information ... t)yj.Proof. (i) Directly calculating yieldsf(t) =mj=1(xj− yj)1txj+ (1 − t)yj−11 + txj+ (1 − t)yjNEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF SYMMETRIC FUNCTIONS 3Theorem...