Báo cáo toán học: " Alspach’s Problem: The Case of Hamilton Cycles and 5-Cycles"

Báo cáo toán học: " Alspach’s Problem: The Case of Hamilton Cycles and 5-Cycles" pps

... decomposition of [1,n4− k − 1] ∪ {n4}ninton4− k Hamilton cycles. We now consider the case of Hamilton cycles and 5 -cycles. The proof of this resultwhen n is odd splits into 2 cases, namely ... h and t with hn + 5t = n(n− 2)/2, the complete graph Kndecomposes intoh Hamilton cycles, t 5 -cycles, and a 1-factor. We also settle Alspach’s problem in the case of Hamilton cycles and 4 -cycles. 1 ... Hamilton cycles the electronic journal of combinatorics 18 (2011), #P82 10 Alspach’s Problem: The Case of Hamilton Cycles and 5 -Cycles Heather JordonDepartment of MathematicsIllinois State UniversityNormal,...

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Báo cáo toán học: " Permutations which are the union of an increasing and a decreasing subsequence" doc

... argumentsjustify the other relations.These lemmas have proved that the disposition of the red, blue, green, and yellow points in the graph of a skew-merged permutation σ is as given inTheorem 1. The next ... the other statementsfollow by symmetry.To complete the proof of Theorem 1 we haveLemma 7 The white points of a permutation are either increasing or de-creasing.Proof From the deﬁnitions of ... arelargest of their colour with respect to “ ”andB,Y are smallest of theircolour (equivalently, G, Y are largest of their colour under “<”andR, B aresmallest of their colour). According to Theorem...

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Báo cáo toán hoc:"Generating functions for the number of permutations with limited displacement." ppsx

... removing the ﬁrst row and the j’thcolumn (j = 1, 2, . . . , d+1) of Ax. By the deﬁnition of T we see that the adjacency matrix of D is exactly T. By Stanley [6, Theorem 4.7.2], the right hand side ... x2).On the o ther hand, if x′ y′, thenx2 y2 and d − 1 − a  d − 1 − b  d − 1 − y2< d − y2 and so x′∈ Yx2,d−y2 and (y′, x′) ∈ Z2.Subcase II.b) 1 < j  m. Theny′= ... 7AcknowledgementMy original proofs in [3] were based on expanding a permanent. It was pointed out by one of the r eferees that the transfer-matrix method gives a more direct and elegant proof of the generating...

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Báo cáo toán học: "Two remarks concerning the theorem of S. Axler, S.-Y. A. Chang and D. Sarason " docx

... class="bi x0 y0 w2 h 1" alt ="" ...

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Báo cáo toán học: "Compact operators in the radical of a reflexive operator algebra " pptx

... ...

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Báo cáo toán học: "Lie groups over the field of rational functions, signed spectral factorization, signed interpolation, and amplifier design " pot

... h 4" alt ="" ...

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Báo cáo toán học: "Compact operators in the algebra of a partially ordered measure space " docx

... ...

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Báo cáo toán học: "A note on the space of pseudodifferential projections with the same principal symbol " pptx

... class="bi x0 y1 w2 h 2" alt ="" ...

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Báo cáo toán học: "A note on the number of (k, )-sum-free sets" potx

... Denoteby SFnk, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal of combinatorics 7 (2000), #R30 7Proof. We need to show that the left-hand side of (4) is ... ϕr)2n/ρ+2n22n/(ρ+1).To complete the proof it is suﬃcient to show that the number of (k, )-sum-free subsets of [1,n] satisfying either (1) or (2) is o(2n/ρ). Denote by B the set of all such subsets, and letB(K, ... case SFn+1,=(1+o(1))2(n+1)/2.Thecaseofk being much larger than  was treated by Calkin and Taylor[4]. They showed that for some constant ck the number of (k, 1)-sum-freesubsets of...

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Báo cáo toán học: "A note on the ranks of set-inclusion matrices" pps

... ﬁeld, and let rF(M) denote the rank of M over F .Theorem. If (k − t) =0intheﬁeldF ,thenrF(Wt,k(v +1))=rF(Wt,k−1(v)) + rF((k − t +1)Wt−1,k(v)). (1)Proof. The block-matrix identityI ... relation is derived for the rank (over most ﬁelds) of the set-inclusionmatrices on a ﬁnite ground set.Given a ﬁnite set X of say v elements, let W = Wt,k(v) be the (0,1)-matrix of inclusionsfor ... k-subsets of X : WT,K=1ifT is contained in K, and 0 otherwise.These matrices play a signiﬁcant part in several combinatorial investigations, see e.g. ([2],Thm. 2.4).Let F be any ﬁeld, and let...

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