Báo cáo toán học: "Matchings Avoiding Partial Patterns" ppsx

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Ngày tải lên: 05/08/2014, 09:46

... square-counting or an interlacing argument, one can show that the max- imum number of vertices in an independent set in the Hoffman-Singleton graph is 15. If S is an independent set of size 15 in this ... Then H is the Hoffman-Singleton graph. Note that we may view the vertices in S as points and the vertices not in S as lines, with a point and line incident if the corresponding verti...

Ngày tải lên: 07/08/2014, 06:20

... played the game with his father.) Two pieces of cut potato can serve as the medium on which to carve the motif and its reflected image, and then these potato stamps are inked and used to produce a ... translations of the translation block. These symmetries add a geometric layer of complexity to the combinatorial scheme. Escher's Case (1) We first consider Escher's case (1), in whi...

Ngày tải lên: 07/08/2014, 06:22

... 33111 322 24 → 331 322 2411 → 331 324 221 1 → 3431 322 211 → 3431 322 211 ∈ [4] 10 (1 12) . (7) the electronic journal of combinatorics 9 (2) (20 02) , #R3 15 Corollary 16 For any p ≥ 0 F v p,0 (x; 2) = e x p  j=0 x j j! . Proof. ... 121 }, {1 12, 121 }, {1 12, 122 }, {1 12, 21 1}, {1 12, 21 2}, {1 12, 22 1}, { 121 , 21 2}. Theorem 5 The pairs {111, 1 12} and {111, 121 } are Wilf e...

Ngày tải lên: 07/08/2014, 07:21

... work of Mansour [14], who computed generating functions for the number of n-permutations that avoid two distinct patterns of length three and contain exactly one copy of another pattern of any length. It ... avoid two distinct patterns of length three and any additional set of patterns. We begin by showing how to enumerate these permuta- tions using generating tre...

Ngày tải lên: 07/08/2014, 07:21

... symbol of σ.Sincen +1>m, we can select a random subsequence of σ of length m by first throwing out one of the n + 1 symbols of σ at random and then randomly selecting a subsequence of length ... the following theorem of Stromquist. We give a proof which is somewhat shorter than the proof in [1], both for its own interest and because we will reuse the method of proof when stu...

Ngày tải lên: 07/08/2014, 08:22

... Waterloo Waterloo, Ontario CANADA N2L 3G1 ipgoulde@math.uwaterloo.ca Curtis Greene Department of Mathematics, Haverford College Haverford, PA 19041 cgreene@haverford.edu Dedicated to Richard Stanley ... a combinatorial explanation for (24) and (25). First, some notation. Since A is defined by a tree, there is a unique (alternating) path between any pair of distinct vertices. For a, b...

Ngày tải lên: 07/08/2014, 08:22

... 2. 3 Proofs of the first two Propositions Proof of Proposition 1. This proof relies on this simple standard algorithm for con- verting a list of all partitions of { 1, ,n} into a list of all partitions ... partitions of { 1, ,n+1}: 1. To each partition of { 1, ,n}, add the 1-member-set { n +1} as a new block. This gives a list of some of the partitions of { 1, ,n+1}. 2. To...

Ngày tải lên: 07/08/2014, 13:21

... Algorithms, and Programming, Version 4.3; Aachen, St. Andrews (1999). the electronic journal of combinatorics 13 (2006), #R88 10 New regular partial difference sets and strongly regular graphs with parameters ... partial difference sets S 1 and S 2 in a group H, the graphs Cay(H, S 1 ) and Cay(H, S 2 ) can be isomorphic. Similarly, for two inequivalent partia...

Ngày tải lên: 07/08/2014, 13:21

... this paper, we consider matchings avoiding partial patterns 1123 and 1132. We give a bijection between 1123 -avoiding matchings with n edges and nonnegative lattice paths from (0, 2) to (2n, 0). ... 1132 -avoiding matchings with n edges and lattice paths from (0, 0) to (2n, 0) starting with an up step. the electronic journal of combinatorics 13 (2006), #R89 2 Matchings avo...

Ngày tải lên: 07/08/2014, 13:21

... 05A05, 05C30 Abstract We show that matchings avoiding a certain partial pattern are counted by the 3- Catalan numbers. We give a characterization of 12312 -avoiding matchings in terms of restrictions ... decompose a 12312 -avoiding matching into smaller 12312 -avoiding matchings. For notational convenience, we denote by E j the edge (i, j) with i < j. Lemma 2.1 Let M be a 12312 -avo...

Ngày tải lên: 07/08/2014, 13:21

... B T C , where A is of size m ì m, B is of size m ì (n m) and C is of size (n m) ì (n m). The sizes of blocks are shown on the margins of the matrix. Let s denote the number of 1’s in B. Then ... elements of π are the last 3 elements of σ, i.e. 5 4 2. The middle part of π is the electronic journal of combinatorics 14 (2007), #R2 8 9 8 7. The first part of π is the permut...

Ngày tải lên: 07/08/2014, 15:22

... electronic journal of combinatorics 15 (2008), #R125 8 Generalizations of Partial Difference Sets from Cyclotomy to Nonelementary Abelian p-Groups John Polhill Department of Mathematics, Computer ... type partial difference sets [3]. We can create a product of such sets with certain Latin square type partial difference sets in nonelementary abelian grou...

Ngày tải lên: 07/08/2014, 21:20

... 121 and 112 are partial- matching equivalent, while 1213 and 1123 are not equivalent. 4 Partial matchings and fill ings of diagrams There is a very close relationship between canonical sequences and ... bijection between -avoiding and τ ′ -avoiding matchings. Since σ and τ are assumed to be partial- matching equivalent, there is a bijection f between σ-avoiding and τ-avoidi...

Ngày tải lên: 08/08/2014, 12:23

... nonsimple critical positions. Keywords: Theory of formal languages; Combinatorics on words; Number The- ory; Partial words; Bordered partial words; Simple border; Simply bordered partial words; Critical ... v is unbordered and is generated by a partial word u, then u is unbordered as well. Hence, every unbordered word over a k-letter alphabet with h holes c an be generat...

Ngày tải lên: 08/08/2014, 14:23