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1.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
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2.
We perform an exact enumeration of the order-preserving maps of fences (zig-zags) and crowns (cycles). From this we derive asymptotic results. 相似文献
3.
Jonathan David Farley 《Order》1995,12(1):5-44
We compute the number of order-preserving and -reversing maps between posets in the class of fences (zig-zags) and crowns (cycles). 相似文献
4.
In this paper we show that the number of positive weights of a quadrature formula is related to the number of rotations of a certain path in the plane. Necessary and sufficient conditions for all weights to be positive can then be obtained. Also, much of classical theory appears in a new light. 相似文献
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6.
An algorithm is presented for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M→R2m, where M is an m-dimensional algebraic manifold. 相似文献
7.
Peter Røgen 《Geometriae Dedicata》2008,134(1):197-202
Given an embedded closed space curve with non-vanishing curvature, its self-linking number is defined as the linking number
between the original curve and a curve pushed slightly off in the direction of its principal normals. We present an index
formula for the self-linking number in terms of the writhe of a knot diagram of the curve and either (1) an index associated
with the tangent indicatrix and its antipodal curve, (2) two indices associated with a stereographic projection of the tangent
indicatrix, or (3) the rotation index (Whitney degree) of a stereographic projection of the tangent indicatrix minus the rotation
index of the knot diagram.
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8.
Jia-yu Shao
Wan-di Wei 《Discrete Mathematics》1992,110(1-3):293-296We establish an explicit formula for the number of Latin squares of order n:
9.
We give a new formula for the winding number of smooth planar curves and show how this can be generalized to curves on closed orientable surfaces. This gives a geometric interpretation of the notion of winding number due to B. Reinhart and D.R.J. Chillingworth. 相似文献
10.
Humio Ichimura 《Archiv der Mathematik》2006,87(6):539-545
Let p be an odd prime number and
. Let
be the classical Stickelberger ideal of the group ring
. Iwasawa [6] proved that the index
equals the relative class number
of
. In [2], [4] we defined for each subgroup H of G a Stickelberger ideal
of
, and studied some of its properties. In this note, we prove that when
mod 4 and [G : H] = 2, the index
equals the quotient
.
Received: 13 January 2006 相似文献
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Gilles Schaeffer 《Journal of Combinatorial Theory, Series A》2008,115(6):903-924
Factorizations of the cyclic permutation into two permutations with respectively n and m cycles, or, equivalently, unicellular bicolored maps with N edges and n white and m black vertices, have been enumerated independantly by Jackson and Adrianov using evaluations of characters of the symmetric group. In this paper we present a bijection between unicellular partitioned bicolored maps and couples made of an ordered bicolored tree and a partial permutation, that allows for a combinatorial derivation of these results.Our work is closely related to a recent construction of Goulden and Nica for the celebrated Harer-Zagier formula, and indeed we provide a unified presentation of both bijections in terms of Eulerian tours in graphs. 相似文献
14.
The decycling number of a graph is the smallest number of vertices which can be removed from so that the resultant graph contains no cycle. A decycling set containing exactly vertices of is called a -set. For any decycling set of a -regular graph , we show that , where is the cycle rank of , is the margin number of , and are, respectively, the number of components of and the number of edges in . In particular, for any -set of a 3-regular graph , we prove that , where is the Betti deficiency of . This implies that the decycling number of a 3-regular graph is . Hence for a 3-regular upper-embeddable graph , which concludes the results in [Gao et al., 2015, Wei and Li, 2013] and solves two open problems posed by Bau and Beineke (2002). Considering an algorithm by Furst et al., (1988), there exists a polynomial time algorithm to compute , the cardinality of a maximum nonseparating independent set in a -regular graph , which solves an open problem raised by Speckenmeyer (1988). As for a 4-regular graph , we show that for any -set of , there exists a spanning tree of such that the elements of are simply the leaves of with at most two exceptions providing . On the other hand, if is a loopless graph on vertices with maximum degree at most , then The above two upper bounds are tight, and this makes an extension of a result due to Punnim (2006). 相似文献
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18.
On the number of summands in the asymptotic formula for the number of solutions to Waring's equation
A. V. Ustinov 《Mathematical Notes》1998,64(2):240-250
In the paper, an estimate of the number of summands in the asymptotic formula for the number of solutions to Waring's equation is obtained. This is achieved by means of a recurrent process leading to a greater reduction than that in Vinogradov's mean value theorem.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 285–296, August, 1998.The author wishes to thank N. M. Korobov for setting the problem and supervising his work. 相似文献
19.
G. G. Rasputin 《Mathematical Notes》1989,45(5):396-400
Translated from Matematicheskie Zametki, Vol. 45, No. 5, pp. 70–75, May, 1989. 相似文献
20.
P. G. Zograf 《Journal of Mathematical Sciences》1982,19(6):1637-1652
In the paper the Selberg trace formula is derived for the Hilbert modular group of a real quadratic algebraic number field with one class of ideals, acting on the product of two upper semiplanes.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 100, pp. 26–47, 1980. 相似文献
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